Question

Use the appropriate change of base formula to convert the given expression to an expression with the indicated base. Round your answer to the nearest ten thousandth if necessary. log 73 base 35

Answer 1

`1.2068`Expalantion:
`\begin{gathered} \text{Given:} \\ \log _(35)\text{ 73} \\ \\ To\text{ apply change of base:} \\ \text{ we will divide the log of the number in base 10 by the log of the base in base 10} \\ \text{for example: log}_ab\text{ = }(\log _(10)b)/(\log _(10)a) \\ \\ In\text{ this case:} \\ \text{ we will divide the log of 73 in base 10 by the log of the base in base 10} \end{gathered}`
`\begin{gathered} \log \text{ of the base = log 35} \\ In\text{ base 10 = }\log _(10)35 \\ \log _(35)73\text{ = }(\log_(10)73)/(\log_(10)35) \end{gathered}`
`\begin{gathered} \log _(35)73\text{ = }(1.86332286)/(1.54406804) \\ \log _(35)73\text{ = 1.2067}6215 \\ To\text{ the nearest ten thousandth,} \\ \log _(35)73\text{ = }1.2068 \end{gathered}`