Question

Find p such that: {(3)^-2}^p=81

Answer 1

Exponential and Logarithmic Equations

Answer:

`p = -2`

Explanation:

Given:

`(3^(-2))^p = 81`

Recall:

`a^b = c \Leftrightarrow \log_a (c) = b`

`\log_a (b^c) = d \Leftrightarrow c \cdot \log_a (b) = d`

Solving for
`p`:

`(3^(-2))^p = 81 \\ ((1)/(3^2))^p = 81 \\ ((1)/(9))^p = 81 \\ \log_(1)/(9) (81) = p \\ p = \log_(1)/(9) (((1)/(81))^(-1)) \\ p = -\log_(1)/(9) ((1)/(81)) \\ p = -(2) \\ p = -2`