What is ln((5x^6)/(11y^7)) ?

The solution to ln((5x^6)/(11y^7)) is ln(5)+6ln(x)-ln(11)-7ln(y)

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simplify ln((5x^6)/(11y^7))

simplify

ln (\frac{5 x ^{6}}{11 y ^{7}})

ln (5) + 6 ln (x) - ln (11) - 7 ln (y)

Solution steps

ln (\frac{5 x ^{6}}{11 y ^{7}})

Apply log rule:

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

ln (\frac{5 x ^{6}}{11 y ^{7}}) = ln (5 x^{6}) - ln (11 y^{7})

= ln (5 x^{6}) - ln (11 y^{7})

Apply log rule:

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

ln (5 x^{6}) = ln (5) + ln (x^{6}), ln (11 y^{7}) = ln (11) + ln (y^{7})

= ln (5) + ln (x^{6}) - (ln (y^{7}) + ln (11))

Apply log rule:

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

ln (x^{6}) = 6 ln (x)

= ln (5) + 6 ln (x) - (ln (11) + ln (y^{7}))

Apply log rule:

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

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

= ln (5) + 6 ln (x) - (ln (11) + 7 ln (y))

- (ln (11) + 7 ln (y)) : - ln (11) - 7 ln (y)

= ln (5) + 6 ln (x) - ln (11) - 7 ln (y)

- lo g_{10} (\frac{0.092}{0.085} \cdot 2.9 \cdot 1 0^{- 8})

ln (\frac{11}{15})

- lo g_{10} (1.7 \cdot 1 0^{- 7})

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

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

What is ln((5x^6)/(11y^7)) ?
The solution to ln((5x^6)/(11y^7)) is ln(5)+6ln(x)-ln(11)-7ln(y)