What is ln(7/(9x^9y)) ?

The solution to ln(7/(9x^9y)) is ln(7)-2ln(3)-9ln(x)-ln(y)

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simplify ln(7/(9x^9y))

simplify

ln (\frac{7}{9 x ^{9} y})

ln (7) - 2 ln (3) - 9 ln (x) - ln (y)

Solution steps

ln (\frac{7}{9 x ^{9} y})

Apply log rule:

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

ln (\frac{7}{9 x ^{9} y}) = ln (7) - ln (9 x^{9} y)

= ln (7) - ln (9 x^{9} y)

Apply log rule:

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

ln (9 x^{9} y) = ln (9) + ln (x^{9}) + ln (y)

= ln (7) - (ln (x^{9}) + ln (y) + ln (9))

Apply log rule:

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

ln (x^{9}) = 9 ln (x)

= ln (7) - (ln (9) + 9 ln (x) + ln (y))

ln (9) = 2 ln (3)

= ln (7) - (9 ln (x) + ln (y) + 2 ln (3))

- (2 ln (3) + 9 ln (x) + ln (y)) : - 2 ln (3) - 9 ln (x) - ln (y)

= ln (7) - 2 ln (3) - 9 ln (x) - ln (y)

ln (\frac{36 5}{25})

lo g_{8} ((\frac{u ^{3}}{v})^{2})

ln (\frac{x}{e ^{4 x}})

ln (\frac{e ^{8}}{15})

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

What is ln(7/(9x^9y)) ?
The solution to ln(7/(9x^9y)) is ln(7)-2ln(3)-9ln(x)-ln(y)