How do you use the Change of Base Formula and a calculator to evaluate the logarithm ${log}_{4} 72$ $log_4 72$ ?

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Answer 1 · 2015-09-24T12:31:06

I found: $3.0849$ $3.0849$

The Change of Base Formula allows you to write:

${log}_{a} b = \frac{{log}_{c} b}{{log}_{c} a}$ $log_ab=(log_cb)/(log_ca)$
and change your base from $a$ $a$ to the new base $c$ $c$ .

We can choose, as new base, $e$ $e$ and use natural logs, $ln$ $ln$ , that can be evaluated using a pocket calculator and get:

${log}_{4} (72) = \frac{ln 72}{ln 4} = 3.0849$ $log_4(72)=(ln72)/(ln4)=3.0849$

How do you use the Change of Base Formula and a calculator to evaluate the logarithm log472log_4 72?