How do I solve for x in the equation 5^x=3125? Also in 5^x=1/125, 9^x=243, 4^x=1/32, and 3*2^x=96?

Answers

Answer 1

Answer: remember
if x^m=x^n and x=x, m=n
also
x^-m=1/(x^m)
(x^m)^n=x^(mn)

try to match bases

5^x=3125
5^x=5^5
x=5

5^x=1/125
1/125=1/(5^3)=5^-3
5^x=5^-3
x=-3

9^x=234
3^(2x)=3^5
2x=5
x=2.5

4^x=1/32
1/32=1/(2^5)=2^-5
2^(2x)=2^-5
2x=-5
x=-2.5

3*2^x=96
first divide both sides by 3
2^x=32
2^x=2^5
x=5

5^x=3125
x=5

5^x=1/125
x=-3

9^x=234
x=2.5

4^x=1/32
x=-2.5

3*2^x=96
x=5

Answer 2

Answer:

5^x=1/125

Take log of both sides

log(5^x)=log(1/125)

x*(log(5))= log(1/125)

x= log(1/125)/ log(25)

x=-3

9^x= 243

Take log of both sides

log(9^x)= log(243)

x*(log(9))= log(243)

x= log(243)/ log(9)

x= 2.5

4^x= 1/32

Take log of

log(4^x)=log(1/32)

x*(log(4))=log(1/32)

x= log(1/32)/log(4)

x= -2.5

3*2^x=96

Divide both sides by 3 so we can make it more simply

3(2^x)/3= 96/3

2^x= 32

Take log of

log(2^X)=log(32)

x(log(2))= log(32)

x= log(32)/log(2)

x=5

As you can see, I only used a simple way for all of them.

I hope that's help:0

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What to numbers multiply to -100 but add up to -21?

When y = x^2, which of the following expressions is
equivalent to –y ?

Answers

-y=-(x^2) because you multiply both sides by -1.

Factor the polynomial.
7x^2 + 68xy - 20y^2

Answers

we notice that it must be a product of 2 different thingummies
so we have
( x+/- y)( x+-/ y)
we need to determine the spaces ad signs
we know that the signs are different since the end result is negative
so fidn the first one
7
factor
7=1 times 7
so we have
(1x+/- y)(7x+/- y)
factor end
-20=-1 and 20 or -2 and 10 or -4 and 5
we want the middle term to be positive so the bigger term must be positive

try the ones closest first
(x-4y)(7x+5y)
multiply out the middles and outers
5xy-28xy is not 68xy
try -2 and 10
(x+10y)(7x-2y)
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ABCDE and FGHJE are similar pentagons. If the perimeter of FGHJE is 7.3, what is the perimeter of ABCDE?

Answers

The answer would be 14.6

How do you know that the answer is 14.6?

Elise built a rectangular vegetable garden that is 9 feet long and has an area of 72 square feet. What is the perimeter of Elise’s vegetable garden?

Answers

Well if you know how long it is, you would divide 72 by 9 giving you 8. So the perimeter wold be calculated by 9+9+8+8=34 feet

Perimeter of a rectangle=2(long)+2(width)

1)we calculate the width.
area=long x width

data:
area =72 ft².
long=9 ft

72 ft²=9 ft * width
width=72 ft²/9 ft=8 ft.

2) we calculate the perimeter.
perimeter=2(9 ft)+2(8 ft)=18 ft + 16 ft=34 ft.

Answer: the perimeter of Elise`s vegetable garden is 34 ft.

Solve the following equations.
1 − log8(x − 3) = log8(2x)

Answers

Answer:

The answer to your question is: 4

Step-by-step explanation:

Data

1 − log₈(x − 3) = log₈(2x)

1 = log₈(x − 3) + log₈(2x)

1 = log₈ 2x(x - 3)

8¹ = 2x(x - 3)

8 = 2x² - 6x

2x² - 6x - 8 = 0

Factorize 2x² - 8x + 2x - 8 = 0

2x(x - 4) + 2(x - 4) = 0

(x - 4) (2x + 2)

x1 = 4 x2 = -2/2 = -1

x2 = -1 is not and answer because there are not negative logs.

A van travels 300 miles on 15 gallons of gas. Find how many gallons the van needs to travel 360 miles.

Answers

Answer: The Van needs 18 gallons of gas to travel 360 miles.

Step-by-step explanation: Given that a Van travels 300 miles on 15 gallons of gas.

We are to find the number of gallons that the Van needs to travel 360 miles.

We will be using the UNITARY method to solve the given problem.

Number of gallons needed to travel 300 miles = 15.

So, number of gallons needed to travel 1 mile will be

$(15)/(300)=(1)/(20).$

Therefore, the number of gallons needed to travel 360 miles is given by

$(1)/(20)* 360=18.$

Thus, the Van needs 18 gallons of gas to travel 360 miles.

Amount of gas required to travel $360\text{ miles}$ is $\boxed{\bf 18\text{\bf\ gallons}}$ .

Further explanation:

The word problems can be solved from the unitary method.

The unitary method is a method in which we have to first find the value of a single unit then further find the required value by multiplying the single unit value.

Given:

A van travelled $300\text{ miles}$ on $15\text{ gallon}$ of gas.

Calculation:

Step 1:

First we have to find the number of gallons in one mile.

It is given that the number of gallons needed to travel $300\text{ miles}$ is equal to $15\text{ gallon}$ .

Use the unitary method to calculate the number of gallons in one mile.

It is calculated as follows:

$\begin{aligned}\text{Number of gallon}&=(15)/(300)\n&=(1)/(20)\end{aligned}$

Step 2:

Now, we have to calculate the number of gallons needed to travel in $360\text{ miles}$ .

Use the unitary method to calculate the required value by multiplying the single unit value.

The number of gallons in one mile is $(1)/(20)$ .

Therefore, the number of gallons in $360\text{ miles}$ is calculated as follow:

$\begin{aligned}\text{Number of gallon}&=(1)/(20)\cdot 360\n&=18\end{aligned}$

Thus, the Van requires $\boxed{\bf 18\text{\bf\ gallons}}$ of gas to travel $360\text{ miles}$ .

Learn more:

1) Learn more about magnitude of the acceleration of the speeding phase brainly.com/question/1597065

2) Learn more about Algebraic expression for the word phrase isbrainly.com/question/1600376

3) Learn more about to solve the equations for the variable brainly.com/question/1682776

Answer details:

Grade: Junior school

Subject: Mathematics

Topic: Unitary method

Keywords: Van, gallons of gases, miles, travels, number of gallons, unitary method, multiply, single unit, linear equation, distance, equation.

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