Question

find the value of x for which 9 power 2x / 9 power -5 = 9 power 13​

Answer 1

Answer:

$\huge \to \tt \red{x = 4}$

Step-by-step explanation:

$\huge \tt \to \frac{ {9}^{2x} }{ {9}^{ - 5} } = {9}^{13} \\ \\ \tt \huge \to {(9)}^{2x - ( - 5)} = {9}^{13} \\ \\ \tt \huge \to {9}^{2x + 5} = {9}^{13} \\ \\ \\ \tt \: when \: bases \: are \: same \: then \: we \: equate \: powers \\ \\ \tt \huge \to2x + 5 = 13 \\ \\ \tt \huge \to2x = 13 - 5 \\ \\ \tt \huge \to2x = 8 \\ \\ \tt \huge \to \: x = \frac{8}{2} = 4$