log96 (1265)

Question

i need to know how to solve this in algebraic way without a calculator. But i am stuck  and cant complete it.

Answer 1

x = log₉₆1265 ⇒

 

96^x = 1265

 

x log(96) =log(1265)  [This is true for any base.  You may work in base 10 if you want.]

 

Then

 

x = log(1265) / log(96)

 

This is an exact solution.  But you may still need to use a calculator to evaluate the 2 logs.