Answers
Given:
[tex]3(4^x)=5^(x+1)[/tex]
To find:
The solution of the given equation.
Solution:
We have,
[tex]3(4^x)=5^(x+1)[/tex]
It can be written as
[tex]3((2^2)^x)=5^(x+1)[/tex]
[tex]3((2^{2x})=5^(x+1)[/tex] [tex][\because (a^m)^n=a^{mn}][/tex]
Taking log on both sides.
[tex]\log [3((2^{2x})]=\log 5^(x+1)[/tex]
[tex]\log 3+ \log ((2^{2x})=\log 5^(x+1)[/tex] [tex][\because \log (ab)=\log a+\log b][/tex]
[tex]\log 3+ 2x\log 2=(x+1)\log 5[/tex] [tex][\because \log x^n=n\log x][/tex]
Putting values of logarithms, we get
[tex]0.477+ 2x(0.301)=(x+1)0.699[/tex] [tex][\because \log 2 =0.301, \log 3=0.477, \log 5=0.699][/tex]
[tex]0.477+ 0.602x=0.699x+0.699[/tex]
[tex]0.602x-0.699x=0.699-0.477[/tex]
[tex]-0.097x=0.222[/tex]
Divide both sides by -0.097.
[tex]x=\dfrac{0.222}{-0.097}[/tex]
[tex]x=-2.288656[/tex]
[tex]x\approx -2.289[/tex]
Therefore, the value of x is -2.289.
Related Questions
Pls help!!!! I will give brainilist
Answers
Answer:
I dont know bhai mara majo gonna be roky
Step-by-step explanation:
no only I did u lolamavo
A carpenter has 10 ½ feet of wooden plank. He cuts off 4 ¼ feet to replace the slat of deck and 3 ⅔ feet to repair a bannister. He uses the rest of the plank to fix a stair. How many feet of wood does the carpenter use to fix the stair?
Answers
Cobra Kai yehdhehdhehehebdhdhdvdgdhdhdhdbdhdbdh
A box of cereal has a width of 4 inches, and a length of 8 inches and a height of 12 inches. What is the volume of the box, in cubic inches?
A box has a width of 4 inches, a length of 8 inches, and a height of 12 inches.
Use the formula V = l w h, where V represents the volume, l represents the length, w represents the width, and h represents the height.
Answers
Answer:
Volume=384 inches squared
Step-by-step explanation:
Multiply the width to the length. Therefore it would be 32. Next you multiply 32 to your height, giving you an answer of 384
Simple. 12in cubed.
Also if u wanted me to be VERY specific as to what 12in cubed equals it would be 1728.
What what is the range for the function f(x)=20x+4
Answers
the points (-5,4)and (1,r) lie on a line with slope -1. Find the missing coordinates r.
Answers
Answer:
R has to be -2
Step-by-step explanation:
So to find a slope the formula is written as
Y2-Y1/ X2 -X1
We know X1 and X2 and Y1.
If we plug those in and put Y2 as the variable ”r”
You’ll get
[tex]\frac{r-4}{1+5}[/tex]
Now make that equal to -1 since thats the slope
If you solve the equation it should get you -2
What is the answer to this math problem it's confusing? 40-(27+3)/2
Answers
Answer:
Anwsers is 25
Step-by-step explanation:
Answer:
25
Step-by-step explanation:
Use the correct order of operations.
40 - (27 + 3)/2 = 40 - 30/2 = 40 - 15 = 25
Answer: 25
2x +18 = 9x + 14 for x.
Answers
Answer:
X= 4/7
Step-by-step explanation:
I used a calculator :)
-7x=-4
X=4/7
Answer 4/7
What is the equation of the line that passes through the point (4,5) with a zero slope?
Answers
Answer:
x=5
Step-by-step explanation:
Since there is no slope, there must be a constant y.
The constant y for this coordinate is 5.
When we have the equation x=5, that creates a straight line through all coordinates with 5 as a y-value.
Can someone help me
Answers
Answer:
ok sooo just go over the grfat and mm count it up to the dot.
Step-by-step explanation:
given the graphs of f(x)=5x+1 and g(x)=x+5, find the solution to this system of equations
y=-5x=1
y-x=5
a. (0,1)
b.(0,5)
c. (1,6)
d. (-5,0)
Answers
Answer:
C. (1,6)
Step-by-step explanation:
y=5x+1
y=x+5
x+5 = 5x+1
4x = 4
x = 1
y = 1 + 5 = 6
(x,y) = (1,6)
• How many terms are in this expression? What
are they?
6x + 4y - 9
Please help
Answers
write - 1/2x+ y = 10 in slope-intercept form,
Answers
Answer:
y = 1/2x + 10
Step-by-step explanation:
y = mx + b (slope intercept form equation)
-1/2x + y = 10
+1/2x +1/2x (What you do to one side must be due to the other)
y = 10 + 1/2x or y = 1/2x + 10 (use to commutative property to swap the terms)
y = 1/2x + 10 (therefore this is in slope intercept form)
shreya has 40 pairs of shoes stacked in boxes if a pair is 2 shoes how many shoes does shreya have
Answers
Answer:
80 shoes
Step-by-step explanation:
40 times 2= 80
will mark brainliest ~ Select the correct answer. Which function is the inverse of f(x)= x^2 – 16 if the domain is
[tex]x \geqslant 0[/tex]
Answers
Step-by-step explanation:
y = x² - 16
x² = y + 16
x = sqrt(y + 16) as x is non-negative.
Therefore f^-1(x) = sqrt(x + 16). (A)
Answer:
the answer is A
Step-by-step explanation:
what type of transformation is described by (x,y)-(x+2,y+3)
Answers
Answer:
reflection across the x axis.
Step-by-step explanation:
When you reflect a point across the line y = x, the x-coordinate and y-coordinate change places. If you reflect over the line y = -x, the x-coordinate and y-coordinate change places and are negated (the signs are changed). the line y = x is the point (y, x). the line y = -x is the point (-y, -x).
The lifespans of gorillas in a particular zoo are normally distributed. The average gorilla lives 20.8 years; the standard deviation is 3.1 years. Use the empirical rule (68-95-99.7\%) to estimate the probability of a gorilla living between 11.5 and 27 years.
Answers
Answer:
go to a called math and way but without the space or the and
Step-by-step explanation:
Answer:
97.35%
Step-by-step explanation:
Khan academy
Lena makes home deliveries of groceries for a supermarket. Her only stops after she leaves the supermarket are at traffic lights and the homes where she makes the deliveries. The graph shows her distance from the store on her first trip of the day.
Give the domain of the function and relate the domain to the relationship described
Answers
made at traffic lights? Answer: 3
1/4 , 1, 4, 16, 64, ________, ________, ________
Answers
Answer:
256, 1024, 4096
Step-by-step explanation:
Multiply the number by 4 to get the next one.
Brainliest please
For f(x) = 4x + 1 and g(x) = x ^ 2 - 5 , find (f o g)(4)
Answers
Step-by-step explanation:
(f o g)(x)
= f(x² - 5)
= 4(x² - 5) + 1
= 4x² - 19.
Therefore (f o g)(4) = 4(4)² - 19 = 64 - 19 = 45.
Answer:
[tex]\boxed {\boxed {\sf 45}}[/tex]
Step-by-step explanation:
When solving a composition of function composition, work from the inside to the outside.
We have the composition:
(f o g)(4)We must start on the inside, and find g(4) first.
1. g(4)
The function for g is:
[tex]g(x)=x^2-5[/tex]
Since we want to find g(4), we have to substitute 4 in for x.
[tex]g(4)=(4)^2-5[/tex]
Solve according to PEMDAS: Parentheses, Exponents, Multiplication, Addition, and Subtraction. First we should solve the exponent.
(4)²= 4*4= 16[tex]g(4)=16-5[/tex]
Subtract 5 from 16.
[tex]g(4)= 11[/tex]
Now, since g(4) equals 11, we have:
(f o g)(4)= f(11)2. f(11)
The function for f is:
[tex]f(x)= 4x+1[/tex]
We want to find f(11), so substitute 11 in for x.
[tex]f(11)= 4(11)+1[/tex]
Solve according to PEMDAS and multiply first.
[tex]f(11)= 44+1[/tex]
Add.
[tex]f(11)= 45[/tex]
(f o g)(4) is equal to 45.
If six people share 4 pints of lemonade equally, how much lemonade will each person receive?
Answers
Answer:
1.5
i think
Step-by-step explanation:
Write the algebraic expression for...
The product of a number x and 10
Answers
Answer:
10x
Step-by-step explanation:
product In math means multiplication, whiles and means addition
50KM into CM.Full step pls
Answers
Answer:
Step-by-step explanation:
1km = 100000cm
50 km = 50 x 100000 = 5000000cm
On a scavenger hunt, you find 19 out of 20 objects. Write "19 out of 20" as a fraction, a decimal, and a percent
Answers
Fraction: 19/20
Decimal: 0.95
Percent: 95%
Last year, Nancy bought a mountain bike for $570. Her bike has depreciated since she bought it. It is now worth $410. What percent did the value of Nancy’s bike depreciate over the past year? Round the the nearest whole percent.
Answers
1) Graph the quadratic function given in standard form and identify the key features. Include at least 5 points on your
graph.
y = -x2 - 2x + 1
Axis of Symmetry:
Vertex:
Y-intercept:
Domain:
Range:
Answers
Answer:
Please find attached the graph of the quadratic function is created using Microsoft Excel
1) The line of symmetry is x = -1
2) The vertex is (-1, 2)
3) The y-intercept is (0, 1)
4) The domain is -∞ ≤ x ≤ ∞
5) The range is 2 ≥ y ≥ -∞
Step-by-step explanation:
The given equation is y = -x² - 2·x + 1
The general vertex form is y = a·(x - h)² + k
h = -b/(2·a) = 2/(-2) = -1
k = f(h) = -(-1)² - 2×(-1) + 1 = 2
Therefore;
1) The line of symmetry goes through the vertex and the line of symmetry is x = -1
2) The vertex = (h, k) = (-1, 2)
3) The y-intercept is the coordinate of the point where x = 0 which is (0, 1)
4) The domain are the possible x-values, therefore, the domain = -∞ ≤ x ≤ ∞
5) The range is the possible values y-values.
From the graph, we have the range = 2 ≥ y ≥ -∞
The graph of the quadratic function is created using Microsoft Excel by generating y-values based on the equation and using the graphing function to insert a two dimensional graph of the generated combination of x and y values as shown in the attached figure.
Ruth is at the park standing next to a slide.
Ruth is 5 feet tall, and her shadow is 3 feet
long. If the shadow of the slide is 7.5 feet
long, what is the height of the slide? Assume
the triangles are similar.
Answers
Answer:
The slide is approximately 12.75 feet.
Step-by-step explanation:
We know that Ruth is 5 feet tall, and her shadow is 3 feet tall.
5 ÷ 3 = 1.7 when rounded to the nearest tenth
Therefore, the shadow height of an object multiplied by 1.7 is the height of the actual object.
If the shadow of the slide is 7.5 feet, we need to multiply 7.5 by 1.7.
7.5 x 1.7 = 12.75
Therefore, the slide is approximately 12.75 feet.
Hope this helps! :D
plzzzzzzzzzzzzzzzzzzzzzzzz
Answers
Find the distance between the two points. Write your answer as a decimal rounded to the hundredths place if needed.
(-9,1) and (-10, -11)
Answers
Answer:
12.04Step-by-step explanation:
The distance between two points can be found by using the formula
[tex]d = \sqrt{ ({x_1 - x_2})^{2} + ({y_1 - y_2})^{2} } \\[/tex]
From the question we have
[tex]d = \sqrt{ ({ - 9 - - 10})^{2} + ({1 - - 11})^{2} } \\ = \sqrt{ ({ - 9 + 10})^{2} + ({1 + 11})^{2} } \\ = \sqrt{ {1}^{2} + {12}^{2} } \\ = \sqrt{1 + 144} \\ = \sqrt{145} \: \: \: \: \: \: \: \: \\ = 12.041594[/tex]
We have the final answer as
12.04 to the nearest hundredthHope this helps you
an article bought for rupees 350 is sold at a profit of 20% find its selling price
Answers
Answer:
420
Step-by-step explanation:
20 percent of 350 is 70, so adding that on will give us the price it is sold at for profit of 70 (20%).
Answer:
350 is our cost price and if we add our proft we get selling price
our profit=( 20/100)×350
i.e.70 so our profit is 70
then,
350+70= selling price
we get 420 as selling price
Need help someone please help me!!
Answers
Step-by-step explanation:
g(r) = 25 - 3r
When r = 4, g(4) = 25 - 3(4) = 25 - 12 = 13.
Answer:
[tex]\boxed{\pink{\sf The\ required\ answer\ is\ 13 .}}[/tex]
Step-by-step explanation:
According to the Question , a function is given to us which is ,
[tex]\implies g(r) = 25 - 3r [/tex]
And we need to find the value of g(4) . So , substituting r = 4 , we have ;
[tex]\implies g(r) = 25 - 3r \\\\\implies g(4) = 25 - 3(4) \\\\ \implies g(4) = 25 - 12 \\\\\boxed{\red{\tt\implies g(4) = 13 }}[/tex]
Hence the required answer is 13.