What is ln(x^2-81)-ln(x^2-6x-27) ?

The solution to ln(x^2-81)-ln(x^2-6x-27) is ln((x+9)/(x+3))

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simplify ln(x^2-81)-ln(x^2-6x-27)

simplify

ln (x^{2} - 81) - ln (x^{2} - 6 x - 27)

ln (\frac{x + 9}{x + 3})

Solution steps

ln (x^{2} - 81) - ln (x^{2} - 6 x - 27)

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln (x^{2} - 81) - ln (x^{2} - 6 x - 27) = ln (\frac{x ^{2} - 81}{x ^{2} - 6 x - 27})

= ln (\frac{x ^{2} - 81}{x ^{2} - 6 x - 27})

Simplify

\frac{x ^{2} - 81}{x ^{2} - 6 x - 27} : \frac{x + 9}{x + 3}

= ln (\frac{x + 9}{x + 3})

lo g_{b} (x^{2} y)

ln (\frac{3 x}{x ^{2} + 1})

lo g_{a} (\frac{x ^{5}}{y z ^{6}})

5 lo g_{93} (3)

2 ln (x) - \frac{3}{2} ln (y) + \frac{1}{2} ln (z)

What is ln(x^2-81)-ln(x^2-6x-27) ?
The solution to ln(x^2-81)-ln(x^2-6x-27) is ln((x+9)/(x+3))