What is log_{3}(x^2-16)-2log_{3}(x+4) ?

The solution to log_{3}(x^2-16)-2log_{3}(x+4) is log_{3}((x-4)/(x+4))

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simplify log_{3}(x^2-16)-2log_{3}(x+4)

simplify

lo g_{3} (x^{2} - 16) - 2 lo g_{3} (x + 4)

lo g_{3} (\frac{x - 4}{x + 4})

Solution steps

lo g_{3} (x^{2} - 16) - 2 lo g_{3} (x + 4)

Apply log rule:

b \cdot lo g_{a} (x) = lo g_{a} (x^{b})

- 2 lo g_{3} (x + 4) = - lo g_{3} ((x + 4)^{2})

= lo g_{3} (x^{2} - 16) - lo g_{3} ((x + 4)^{2})

Apply log rule:

lo g_{a} (x) - lo g_{a} (y) = lo g_{a} (\frac{x}{y})

lo g_{3} (x^{2} - 16) - lo g_{3} ((x + 4)^{2}) = lo g_{3} (\frac{x ^{2} - 16}{( x + 4 ) ^{2}})

= lo g_{3} (\frac{x ^{2} - 16}{( x + 4 ) ^{2}})

Simplify

\frac{x ^{2} - 16}{( x + 4 ) ^{2}} : \frac{x - 4}{x + 4}

= lo g_{3} (\frac{x - 4}{x + 4})

lo g_{10} (\frac{1}{2 ^{n}})

- lo g_{10} (8.3 \cdot 1 0^{- 5})

lo g_{10} (14) - lo g_{10} (7)

ln (3) + 4 ln (x)

lo g_{10} (\frac{p ^{4} + q}{100})

What is log_{3}(x^2-16)-2log_{3}(x+4) ?
The solution to log_{3}(x^2-16)-2log_{3}(x+4) is log_{3}((x-4)/(x+4))