What is ln((x^8)/(sqrt(x^2-25))) ?

The solution to ln((x^8)/(sqrt(x^2-25))) is 8ln(x)-ln(sqrt(x^2-25))

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simplify ln((x^8)/(sqrt(x^2-25)))

simplify

ln (\frac{x ^{8}}{x ^{2} - 25})

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

Solution steps

ln (\frac{x ^{8}}{x ^{2} - 25})

Apply log rule:

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

ln (\frac{x ^{8}}{x ^{2} - 25}) = ln (x^{8}) - ln (x^{2} - 25)

= ln (x^{8}) - ln (x^{2} - 25)

Apply log rule:

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

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

= 8 ln (x) - ln (x^{2} - 25)

ln (\frac{0.234}{239})

ln (\frac{128}{49}) - 25 ln (\frac{10}{7}) + \frac{9}{2}

- ln (6) + ln (5)

- \frac{3 ln ( 2 )}{4}

8.31 \cdot ln (0.7 5^{\frac{1}{0.35}} \cdot 4)

What is ln((x^8)/(sqrt(x^2-25))) ?
The solution to ln((x^8)/(sqrt(x^2-25))) is 8ln(x)-ln(sqrt(x^2-25))