Question

How do I identify the proper steps and evaluating log 7 to the power of 2

Answer 1

1) To evaluate the following logarithm:

`\log _72`

Given:

`\log _74\approx0.712\text{ and }\log _78\approx1.069`

2) Notice that we can rewrite that log of 4 this way, using the quotient property of logarithms:

`\begin{gathered} \log _7((8)/(4))=\log _78-\log _74=\log _72 \\ 1.069\text{ -}0.712\text{ = }0.357 \\ \log _72\approx0.3567 \end{gathered}`

As we know that 8/4 =2, we could rewrite that as above.

3) Hence, the answer is:

`\begin{gathered} 1)\text{ }\log _72\text{ =}\log _7((8)/(4)) \\ 2)\text{ }\log _72=\log _78-\log _74 \\ \end{gathered}`