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#