Question

Need Answer NOW!!! Solve for the following equation step by step and justify your steps when using an exponential property.

Answer 1

x = 5/7

Explanation:

(7^x)^4) = 7^2 * 7^3 / 7^3x

1. Simplify the expression

(7^x)^4) becomes 7^4x

7^2 * 7^3 becomes 7^5

7^5/7^3x becomes 7^5 - 7^3x

Your new equation: 7^4x = 7^5 - 7^3x

2. Since the bases(7) are the same set the exponents equal to each other

4x = 5 - 3x

3. Combine like terms

4x + 3x = 5

7x = 5

4. Divide both sides by 7 to get x by itself

x = 5/7

Answer 2

x =
`(5)/(7)`

Explanation:

`(7^(x))^(4)=(7^(2)* 7^(3))/(7^(3x))`

`(7^(x))^(4)=(7^((2+3)))/(7^(3x))` [Since
`a^(b)* a^(c)=a^(b+c)` ]

`7^(4x)=(7^(5))/(7^(3x))` [since
`(a^(b))^(c)=a^(bc)` ]

`7^(4x)={7^(5)*{7^(-3x)}` [
`(1)/(a)=a^(-1)` ]

`7^(4x)=7^((5-3x))`

4x = 5 - 3x

`4x+3x=5` ⇒ 7x = 5

x =
`(5)/(7)`