Math CentralQuandaries & Queries


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

\[\ln 3^x = \ln 14\]


\[x \ln 3 = \ln 14.\]

dividing both sides by $\ln 3$ yields

\[x = \frac{\ln 14}{\ln 3}.\]

Now use your calculator.


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