Best solutions to - "Write the exprissuon as a sum and/or difference..."

aflacatn

Answered question

2021-08-10

Write the exprissuon as a sum and/or difference of logarithms.

\log (\frac{7 \sqrt{x + 3}}{x^{4} {(x - 5)}^{2}}) x > 5

Ayesha Gomez

Skilled2021-08-11Added 104 answers

Now

\log (\frac{7 \sqrt{x + 3}}{x^{4} {(x - 5)}^{2}}) x > 5

= \log (7 \sqrt{x + 3}) - \log (x^{4} {(x - 5)}^{2}) [∵ \log (\frac{m}{n}) = \log m - \log n]

= \log (7) + \log (\sqrt{x + 3}) - \log (x 4) - {\log (x - 5)}^{2} [\log (m n) = \log m + \log n]

= \log (7) + \frac{1}{2} {\log (x + 3)}^{\frac{1}{2}} - 4 \log x - 2 \log (x - 5) [{\log x}^{m} = m \log x]

= \log (7) + \frac{1}{2} \log (x + 3) - 4 \log x - 2 \log (x - 5)

Hence

\log (\frac{7 \sqrt{x + 3}}{x^{4} {(x - 5)}^{2}}) = \log (7) + \frac{1}{2} \log (x + 3) - 4 \log x - 2 \log (x - 5)

Do you have a similar question?

Recalculate according to your conditions!

Didn't find what you were looking for?