Question

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

Answer 1

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

using the ' laws of exponents '

• $a^{m}$ × $a^{n}$ = $a^{( m + n )}$

•  $a^{m}$ ÷ $a^{n}$ = $a^{(m - n)}$

• ($a^{m}$)^n = $a^{mn}$

$7^{2}$ × $7^{3}$ = $7^{5}$ ÷ $7^{3x}$ = $7^{5 - 3x}$

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

equating the exponents since bases on both sides are 7

4x = 5 - 3x

7x = 5 ⇒ x =$\frac{5}{7}$