What is ln((13x^8)/(y^5)) ?

The solution to ln((13x^8)/(y^5)) is ln(13)+8ln(x)-5ln(y)

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simplify ln((13x^8)/(y^5))

simplify

ln (\frac{13 x ^{8}}{y ^{5}})

ln (13) + 8 ln (x) - 5 ln (y)

Solution steps

ln (\frac{13 x ^{8}}{y ^{5}})

Apply log rule:

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

ln (\frac{13 x ^{8}}{y ^{5}}) = ln (13 x^{8}) - ln (y^{5})

= ln (13 x^{8}) - ln (y^{5})

Apply log rule:

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

ln (y^{5}) = 5 ln (y)

= ln (13 x^{8}) - 5 ln (y)

Apply log rule:

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

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

= ln (13) + ln (x^{8}) - 5 ln (y)

Apply log rule:

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

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

= ln (13) + 8 ln (x) - 5 ln (y)

lo g_{3} (\frac{1}{2}) + (\frac{1}{2})^{2}

- (\frac{3}{4}) lo g_{2} (\frac{3}{4}) - ((\frac{1}{4}) lo g_{2} (\frac{1}{4}))

ln ∣ 3 x + x ∣ - ln (2 - x)

- \frac{5}{2} ln ∣ u + 5 ∣ + \frac{5}{2} ln ∣ u - 5 ∣

lo g_{b} (u^{9} v^{8})

What is ln((13x^8)/(y^5)) ?
The solution to ln((13x^8)/(y^5)) is ln(13)+8ln(x)-5ln(y)