How do you solve #12^r=13#?

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Answer 1 · 2016-11-25T18:20:44

Please see the explanation.

You can use either the natural logarithm or the base 10 logarithm for this step. (I will use the base 10):

#log_10(12^r) = log_10(13)#

Use the property of all logarithms #log(a^b) = (b)log(a)#:

#(r)log_10(12) = log_10(13)#

Divide both sides by #log_10(12)#:

#r = log_10(13)/log_10(12)#

#r ~~ 1.032#