What is ln(x/(x-8))+ln((x+8)/x)-ln(x^2-64) ?

The solution to ln(x/(x-8))+ln((x+8)/x)-ln(x^2-64) is -ln((x-8)^2)

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simplify ln(x/(x-8))+ln((x+8)/x)-ln(x^2-64)

simplify

ln (\frac{x}{x - 8}) + ln (\frac{x + 8}{x}) - ln (x^{2} - 64)

- ln ((x - 8)^{2})

Solution steps

ln (\frac{x}{x - 8}) + ln (\frac{x + 8}{x}) - ln (x^{2} - 64)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (\frac{x}{x - 8}) + ln (\frac{x + 8}{x}) = ln (\frac{x}{x - 8} \cdot \frac{x + 8}{x})

= ln (\frac{x}{x - 8} \cdot \frac{x + 8}{x}) - ln (x^{2} - 64)

Simplify

\frac{x}{x - 8} \cdot \frac{x + 8}{x} : \frac{x + 8}{x - 8}

= ln (\frac{x + 8}{x - 8}) - ln (x^{2} - 64)

Apply log rule:

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

ln (\frac{x + 8}{x - 8}) - ln (x^{2} - 64) = ln (\frac{\frac{x + 8}{x - 8}}{x ^{2} - 64})

= ln (\frac{\frac{x + 8}{x - 8}}{x ^{2} - 64})

Simplify

\frac{\frac{x + 8}{x - 8}}{x ^{2} - 64} : \frac{1}{( x - 8 ) ^{2}}

= ln (\frac{1}{( x - 8 ) ^{2}})

Apply log rule:

lo g_{a} (\frac{1}{x}) = - lo g_{a} (x)

= - ln ((x - 8)^{2})

- 3 + (- 5)

\frac{10}{2 i}

x^{2} + 81 < 18 x

(t^{- 2})^{6}

3 (2 x + 3) = - 5 x

What is ln(x/(x-8))+ln((x+8)/x)-ln(x^2-64) ?
The solution to ln(x/(x-8))+ln((x+8)/x)-ln(x^2-64) is -ln((x-8)^2)