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

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

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

expand

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

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

Solution steps

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

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

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

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

Apply log rule:

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

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

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

\frac{x ^{7}}{x ^{2} - 25} = \frac{x ^{7} x ^{2} - 25}{x ^{2} - 25}

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

- lo g_{10} (2.62 \cdot 1 0^{- 6})

- lo g_{10} (1.89 (1 0^{- 3}))

ln (x^{2} e^{3})

ln (π (0.6339))

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