Problem

Write the following as the sum and/or difference of logarithms. Assume all variables are positive.
\[
\log \left(\frac{8 y}{7}\right)=
\]

The answer format in lowercase characters is: $\log$ (number)

Answer

Expert–verified
Hide Steps
Answer

Final Answer: \(\boxed{\log(8) + \log(y) - \log(7)}\)

Steps

Step 1 :Assume y to be a positive number

Step 2 :Calculate the logarithms: \(\log(8) = 2.0794415416798357\), \(\log(y) = 0.0\), \(\log(7) = 1.9459101490553132\)

Step 3 :Calculate the final expression: \(2.0794415416798357 + 0.0 - 1.9459101490553132 = 0.13353139262452252\)

Step 4 :The numerical value of the expression when y is assumed to be 1 is approximately 0.1335

Step 5 :The final answer is the expression we derived earlier: \(\log(8) + \log(y) - \log(7)\)

Step 6 :Final Answer: \(\boxed{\log(8) + \log(y) - \log(7)}\)

link_gpt