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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

$x = \frac{\ln 14}{\ln 3}.$