how do I solve a logarithm problem as shown

Question

How do I solve this log problem step by step?

log problem

I have been struggling with how to show my work on this.

thank you

Margaret

Answer 1

We know $\log_{b} a =\frac {\log a}{\log b} $ and that $\log ab = \log a +\log b $. Now we thus get, $$14\log_{14}(6) = 14\frac{\log 6}{\log 14} =14\frac {\log 2 +\log 3}{\log 2 +\log 7} $$ Hope it helps.