Question

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

Answer 1

Answer:

x = 5/7

Step-by-step 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

Answer:

x = $\frac{5}{7}$

Step-by-step explanation:

$(7^{x})^{4}=\frac{7^{2}\times 7^{3}}{7^{3x}}$

$(7^{x})^{4}=\frac{7^{(2+3)}}{7^{3x}}$ [Since $a^{b}\times a^{c}=a^{b+c}$ ]

$7^{4x}=\frac{7^{5}}{7^{3x}}$ [since $(a^{b})^{c}=a^{bc}$ ]

$7^{4x}={7^{5}\times{7^{-3x}}$  [ $\frac{1}{a}=a^{-1}$ ]

$7^{4x}=7^{(5-3x)}$

4x = 5 - 3x

$4x+3x=5$ ⇒ 7x = 5

x = $\frac{5}{7}$