How do you use the Change of Base Formula and a calculator to evaluate the logarithm log_4 72log472?

1 Answer

Refer to explanation

Explanation:

Using the change of base of formula

log_(4)72=log72/log4=log(9*8)/log(2^2)=(2*log3+3*log2)/(2*log2)= 3/2+log3/log2log472=log72log4=log(98)log(22)=2log3+3log22log2=32+log3log2

Now using a calculator we see that log2=0.69log2=0.69 and log3=1.10log3=1.10

so finally log_4 72=3.08log472=3.08