What is ln(13)+8ln(x)-2ln(y) ?

The solution to ln(13)+8ln(x)-2ln(y) is ln((13x^8)/(y^2))

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simplify ln(13)+8ln(x)-2ln(y)

simplify

ln (13) + 8 ln (x) - 2 ln (y)

ln (\frac{13 x ^{8}}{y ^{2}})

Solution steps

ln (13) + 8 ln (x) - 2 ln (y)

Apply log rule:

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

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

= ln (13) + ln (x^{8}) - 2 ln (y)

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (13) + ln (x^{8}) = ln (13 x^{8})

= ln (13 x^{8}) - 2 ln (y)

Apply log rule:

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

2 ln (y) = ln (y^{2})

= ln (13 x^{8}) - ln (y^{2})

Apply log rule:

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

ln (13 x^{8}) - ln (y^{2}) = ln (\frac{13 x ^{8}}{y ^{2}})

= ln (\frac{13 x ^{8}}{y ^{2}})

- ln \frac{8}{3} + \frac{8}{3} 2 + ln \frac{2}{3} + \frac{8}{3} 2 + C

\frac{1}{2} lo g_{10} (n) + 3 lo g_{10} (m)

lo g_{u} (u^{- 7}) + 5 lo g_{u} (u^{\frac{2}{5}})

lo g_{2} (5) + lo g_{2} (6)

lo g_{b} (\frac{1.792}{1.946})

What is ln(13)+8ln(x)-2ln(y) ?
The solution to ln(13)+8ln(x)-2ln(y) is ln((13x^8)/(y^2))