What is ln((x^6)/(sqrt(x^2-25))) ?

The solution to ln((x^6)/(sqrt(x^2-25))) is 6ln(x)-ln(sqrt(x^2-25))

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simplify ln((x^6)/(sqrt(x^2-25)))

simplify

ln (\frac{x ^{6}}{x ^{2} - 25})

6 ln (x) - ln (x^{2} - 25)

Solution steps

ln (\frac{x ^{6}}{x ^{2} - 25})

Apply log rule:

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

ln (\frac{x ^{6}}{x ^{2} - 25}) = ln (x^{6}) - ln (x^{2} - 25)

= ln (x^{6}) - ln (x^{2} - 25)

Apply log rule:

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

ln (x^{6}) = 6 ln (x)

= 6 ln (x) - ln (x^{2} - 25)

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What is ln((x^6)/(sqrt(x^2-25))) ?
The solution to ln((x^6)/(sqrt(x^2-25))) is 6ln(x)-ln(sqrt(x^2-25))