Write as the sum andor difference of logarithms. Express powers as factors. log4(x+6x7) A. log4(x+6)−log4x B. 7log4x−log4(x+6) C. log4(x+6)−7log4x D. log4(x+6)+7log4x

"Write as the sum and\or difference of logarithms...." was answered by our community

Brennan Flores

2021-07-31

Write as the sum and\or difference of logarithms. Express powers as factors.

\log_{4} (\frac{x + 6}{x^{7}})

\log_{4} (x + 6) - \log_{4} x

7 \log_{4} x - \log_{4} (x + 6)

\log_{4} (x + 6) - 7 \log_{4} x

\log_{4} (x + 6) + 7 \log_{4} x

davonliefI

Skilled2021-08-01Added 79 answers

Step 1
Given,

\log_{4} (\frac{x + 6}{x^{7}})

Step 2
Property used:

\log_{a} (\frac{m}{n}) = \log_{a} m - \log_{a} n

\log_{a} m^{n} = n \log_{a} m

Step 3
Apply the above property, we get

\Rightarrow \log_{4} (x + 6) - \log_{4} (x^{7})

\Rightarrow \log_{4} (x + 6) - 7 \log_{4} (x)

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