How do you use the Change of Base Formula and a calculator to evaluate the logarithm $log_9 3$ ?

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Answer 1 · 2015-08-30T14:13:03

With a calculator you can use $log = log_10$ or $ln = log_e$ with the change of base formula to find answer $0.5$

Alternatively use $log_3$ to find $1/2$ algebraically.

The change of base formula tells you that $log_a b = (log_c b)/(log_c a)$

So you can use: $log_9 3 = (log 3)/(log 9)$ with common logarithms.

On a calculator this will give:

$(log 3) / (log 9) ~~ 0.4771212547 / 0.9542425094 ~~ 0.5$

Or you can use $log_9 3 = (ln 3)/(ln 9)$ with natural logarithms.

$(ln 3) / (ln 9) ~~ 1.0986122887 / 2.197224577 ~~ 0.5$

Alternatively, just do the algebra using $log_3$ :

$log_9 3 = (log_3 3) / (log_3 9) = (log_3 3^1) / (log_3 3^2) = 1/2$

How do you use the Change of Base Formula and a calculator to evaluate the logarithm log_9 3log_9 3?