What is log_{10}(x^2-16)-2log_{10}(x+4) ?

The solution to log_{10}(x^2-16)-2log_{10}(x+4) is log_{10}((x-4)/(x+4))

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simplify log_{10}(x^2-16)-2log_{10}(x+4)

simplify

lo g_{10} (x^{2} - 16) - 2 lo g_{10} (x + 4)

lo g_{10} (\frac{x - 4}{x + 4})

Solution steps

lo g_{10} (x^{2} - 16) - 2 lo g_{10} (x + 4)

Apply log rule:

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

- 2 lo g_{10} (x + 4) = - lo g_{10} ((x + 4)^{2})

= lo g_{10} (x^{2} - 16) - lo g_{10} ((x + 4)^{2})

Apply log rule:

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

lo g_{10} (x^{2} - 16) - lo g_{10} ((x + 4)^{2}) = lo g_{10} (\frac{x ^{2} - 16}{( x + 4 ) ^{2}})

= lo g_{10} (\frac{x ^{2} - 16}{( x + 4 ) ^{2}})

Simplify

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

= lo g_{10} (\frac{x - 4}{x + 4})

2 lo g_{10} (x) + 3 lo g_{10} (x + 1)

\frac{1}{3} lo g_{10} (a) - \frac{2}{5} lo g_{10} (b)

lo g_{10} (2) + lo g_{10} (3) - lo g_{10} (5)

ln (\frac{10 x ^{4}}{( 4 x ^{3} - 6 ) ^{2}})

ln (cos (x)) - ln (sin (x))

What is log_{10}(x^2-16)-2log_{10}(x+4) ?
The solution to log_{10}(x^2-16)-2log_{10}(x+4) is log_{10}((x-4)/(x+4))