Question

Use the change-of-base formula to write the logarithmic expression as an expression using only logarithms with base 10.log, Xsm TutorialxDid you find the quotient of the common logarithm of both parts of the logarithmic expression?Submit Answer

Answer 1

`(\log_(10)x)/(\log_(10)9)`Step-by-step explanation:

`\begin{gathered} \text{Given: log}_9x \\ To\text{ use change of base to convert to base 10} \end{gathered}`

Applying change of base formula:

`\begin{gathered} \log _ba\text{ to base c:} \\ \log _ba\text{ = }\frac{\log_c\text{ a}}{\log_c\text{ b}} \end{gathered}`
`\begin{gathered} \text{We apply same procedure to }\log _9x\colon \\ \text{converting to base 10:} \\ \log _9x\text{ = }(\log_(10)x)/(\log_(10)9) \\ \end{gathered}`