Question

Evaluate the following expression. Round your answer to two decimal places.log7 9A.0.95B.1.13C.2.20D.0.89

Answer 1

Step-by-step explanation

we are asked to evaluate

`log_79^(\:)`

We will follow the steps below

`\begin{gathered} step\text{ 1} \\ \mathrm{Factor\:the\:number:\:}\:9=3^2 \\ \\ log_79=\log_7\left(3^2\right) \end{gathered}`

`\begin{gathered} step\text{ 2} \\ \mathrm{Apply\:log\:rule}:\quad \log _a\left(x^b\right)=b\cdot \log _a\left(x\right),\:\quad \:x>0 \\ \\ \log _7\left(3^2\right)=2\log _7\left(3\right) \\ \end{gathered}`

`\begin{gathered} step\text{ 3} \\ \\ simplify \\ \\ 2\log_7\left(3\right)=1.129 \end{gathered}`

Therefore, the answer is 1.13