Question

Use the Change of Base Formula to evaluate log(8)77

Answer 1

These are my choices...
3.467
1.886
4.344
2.089

Answer 2

Similar Problem:


\[\Large \log_{5}(32) = \frac{\log(32)}{\log(5)}\]


\[\Large \log_{5}(32) = \frac{1.505149978}{0.6989700043}\]


\[\Large \log_{5}(32) = 2.153382790\]

Answer 3

so it would be 2.0889 ?

Answer 4

good,


\[\Large \log_{8}(77) = \frac{\log(77)}{\log(8)}\]


\[\Large \log_{8}(77) = \frac{1.88649072517249}{0.90308998699194}\]


\[\Large \log_{8}(77) = 2.0889288468983\]

Answer 5

Remember the formula\[\log_a(M)=\frac{\log_b(M)}{\log_b(a)}\]So\[\log_8(77)=\frac{\log77}{\log8}=\frac{\ln77}{\ln8}\]

Answer 6

(: thanks

Answer 7

For a simpler way to solve, consider that \[8^2=64<77<8^3=512 \implies 2<\log_877<3\]which leads you directly to only one of your possible answers.