Question

I literally need so much help

Angie is working on solving the exponential equation 23x = 6; however, she is not quite sure where to start. Using complete sentences, describe to Angie how to solve this equation.

Hint: Use the change of base formula: log base b of y equals log y over log b.

Answer 1

`x=(\log 6)/(\log 23)`

Explanation:

Given exponential equation:

`23^x=6`

`\textsf{Apply the log law}: \quad a^c=b \iff \log_ab=c`

`\implies\log_(23)6=x`

`\textsf{Given change of base formula}: \quad \log_by=(\log y)/(\log b)}`

Apply the given change of base formula:

`\implies x=(\log 6)/(\log 23)`