Question

Angie is working on solving an exponential equation 23^x=6; however, she’s not quite sure where to start. Using complete sentences, describe to Angie how to solve this equation using the change of base formula.

Answer 1

we have the equation

`23^x=6`

Remember the definition of logarithm

`\begin{gathered} If \\ a^x=b \\ then \\ x=\log_ab \end{gathered}`

Applying the definition of a logarithm to this problem

we have that

`x=\log_(23)6`

Apply change of base formula

Remember that

`\log_bM=(\log_(10)M)/(\log_(10)b)=(logM)/(logb)`

so

`\log_(23)6=(log6)/(log23)`

therefore

The answer is

`x=(log6)/(log23)`