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Section 1.8 : Logarithm Functions
13. Use the change of base formula and a calculator to find the value of \({\log _{12}}35\).
Show SolutionWe can use either the natural logarithm or the common logarithm to do this so we’ll do both.
\[{\log _{12}}35 = \frac{{\ln 35}}{{\ln 12}} = \frac{{3.55534806}}{{2.48490665}} = \require{bbox} \bbox[2pt,border:1px solid black]{{1.43077731}}\] \[{\log _{12}}35 = \frac{{\log 35}}{{\log 12}} = \frac{{1.54406804}}{{1.07918125}} = \require{bbox} \bbox[2pt,border:1px solid black]{{1.43077731}}\]So, as we noted at the start it doesn’t matter which logarithm we use we’ll get the same answer in the end.