"Write the expression as a sum and/or difference..." was answered by our experts

Alyce Wilkinson

Answered question

2021-08-13

Write the expression as a sum and/or difference of logarithms, express powers as factors:

5 x \frac{3 x + 3}{x^{2}}

broliY

Skilled2021-08-14Added 97 answers

Step 1
Consider the logarithm

\log \frac{5 x (3 x + 3)}{x^{2}}

.
Express the logarithm as sum and or difference of logarithm as follows.

\log \frac{5 x (3 x + 3)}{x^{2}}

= \log \frac{5 (3 x + 3)}{x}

= \log 5 (3 x + 3) - \log x (∵ \log_{b} (m) - \log_{b} (n) = \log_{b} (\frac{m}{n}))

= \log 5 + \log (3 x + 3) - \log x (∵ \log_{b} (m) + \log_{b} (n) = \log_{b} (m n))

Step 2
Answer: The logarithm as sum and or difference of logarithm is

\log 5 + \log (3 x + 3) - \log x

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?