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| Math Central | Quandaries & Queries |
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Question from Tash, a parent: Use the Change of Base Formula and a calculator to evaluate the logarithm, correct to six decimal places. Use either natural or common logarithms. log3 14 |
Hi Tash,
I don't remember formulas!
I would approach your problem this way.
Let \[x = \log_3 14.\]
Raising both sides to the power of $3$ I get
\[3^x = 14.\]
I am going to use natural logarithms and take the logarithm of each side to get
\[\ln 3^x = \ln 14\]
or
\[x \ln 3 = \ln 14.\]
dividing both sides by $\ln 3$ yields
\[x = \frac{\ln 14}{\ln 3}.\]
Now use your calculator.
Penny
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