Question

Write the following logarithm as a quotient of two common logarithms. Do not siplify the quotient.
log_{2}9
Choose the answer below.
1)(log9)/(log2)
2)(log_{8}2)/(log_{8}9)
3)(log_{11}2)/(log_{11}9)
4)(log_{2}9)/(log_{2}8)

Answer 1

To express \( \log_{2} 9 \) as a quotient of two common logarithms, we can use the change of base formula which states:

\[
\log_{b} a = \frac{\log_{k} a}{\log_{k} b}
\]

for any base \( k \). We can choose \( k = 10 \) (common logarithm) to write:

\[
\log_{2} 9 = \frac{\log 9}{\log 2}
\]

Thus, the answer is:

1) \(\frac{\log 9}{\log 2}\)