Question

Evaluate the following logarithms using a calculator and the change of base formula. If necessary, round to 4 decimal places.

Answer 1

d) 2.0574

e) 0.2878

Explanation

Change of base formula

`\log_ab=(\log_cb)/(\log_ca)_`

d) Applying this formula to this case and using a base of 10 in the new logarithms, we get:

`\begin{gathered} \log_(20)475=(\log_(10)475)/(\log_(10)20) \\ \log_(20)475=(2.6767)/(1.3010) \\ \log_(20)475=2.0574 \end{gathered}`

e) Applying this formula to this case and using a base of 10 in the new logarithms, we get:

`\begin{gathered} \log_(15)2.18=(\log_(10)2.18)/(\log_(10)15) \\ \log_(15)2.18=(0.3385)/(1.1761) \\ \log_(15)2.18=0.2878 \end{gathered}`