Question

What is log base 7 of 252

Answer 1

Answer:

2.84

Step-by-step explanation:

Recognize that 252 = 7*36

and so:

log base 7 of 252 = log base 7 of 36 + log base 7 of 7, or

                                 log base 7 of 36 + 1

So the most you can simplify log base 7 of 252 is to write 1 + log base 7 of 36.

Or, if you want to use the change of base formula, you could do the following:

                                 log 36

log base 7 of 36 = -------------- = 1.84

                                  log 7

and so log base 7 of 252 would come out to

1 + log base 7 of 36  =  1 + 1.84  = 2.84

Check:  does 7^2.84 = 252?  YES.  So we know that:

 1 + log base 7 of 36 = 2.84