What is ln(x/(x-8))+ln((x+8)/x) ?

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

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simplify ln(x/(x-8))+ln((x+8)/x)

simplify

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

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

Solution steps

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

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})

Simplify

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

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

\frac{1}{6} \cdot ln (\frac{1}{9 ^{3}})

lo g_{10} (z y^{3})

\frac{1}{2} [ln (3) + 4 ln (x) - 2 ln (x - 1)]

\frac{( 0.5 ln ( 28 ) - ln ( 2 ) )}{0.5}

\frac{1}{2} ln (\frac{11}{3})

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