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 $log_10(12)$ :

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

$r ~~ 1.032$

How do you solve 12^r=1312^r=13?