What is expand ln((x^7)/(sqrt(x^2-25))) ?

The solution to expand ln((x^7)/(sqrt(x^2-25))) is 7ln(x)-ln(sqrt(x^2-25))

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expand ln((x^7)/(sqrt(x^2-25)))

expand

ln (\frac{x ^{7}}{x ^{2} - 25})

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

Solution steps

ln (\frac{x ^{7}}{x ^{2} - 25})

Apply log rule:

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

ln (\frac{x ^{7}}{x ^{2} - 25}) = ln (x^{7}) - ln (x^{2} - 25)

= ln (x^{7}) - ln (x^{2} - 25)

Apply log rule:

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

ln (x^{7}) = 7 ln (x)

= 7 ln (x) - ln (x^{2} - 25)

- lo g_{10} (1.58 \cdot 1 0^{- 6})

ln \frac{r}{2} + 1 - ln \frac{r}{2} - 1

ln 3 - 2 - ln - 3 - 2

\frac{7 ln ( 2 ) - ln ( 12.8 )}{ln ( 36.1 ) - ln ( 22 )}

What is expand ln((x^7)/(sqrt(x^2-25))) ?
The solution to expand ln((x^7)/(sqrt(x^2-25))) is 7ln(x)-ln(sqrt(x^2-25))