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Popular >

simplify ln(4/(9x^9y))

Solution

simplify

ln (\frac{4}{9 x ^{9} y})

Solution

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

Solution steps

ln (\frac{4}{9 x ^{9} y})

Apply log rule:

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

ln (\frac{4}{9 x ^{9} y}) = ln (4) - ln (9 x^{9} y)

= ln (4) - 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 (4) - (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 (4) - (ln (9) + 9 ln (x) + ln (y))

ln (9) = 2 ln (3)

= ln (4) - (9 ln (x) + ln (y) + 2 ln (3))

ln (4) = 2 ln (2)

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

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

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

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Frequently Asked Questions (FAQ)

What is ln(4/(9x^9y)) ?
The solution to ln(4/(9x^9y)) is 2ln(2)-2ln(3)-9ln(x)-ln(y)