Question

How do you use change of base to simplify `log_7 83`?

Answer 1

You use the fact that:
`log_aM=ln(M)/ln(a)`
In your case you have:
`log_7(83)=ln(83)/ln(7)=2.271`
That can be evaluated with a normal calculator.

You can now check your result writing:
`7^(2.271)=83.026..~~83`

(I use `ln`, the natural log, but you can use the other log that your calculator uses, the one in base 10, the result is the same, try it)

Hope it helps