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Popular >

simplify ln(1/(x^5y^5))

Solution

simplify

ln (\frac{1}{x ^{5} y ^{5}})

Solution

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

Solution steps

ln (\frac{1}{x ^{5} y ^{5}})

Apply log rule:

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

ln (\frac{1}{x ^{5} y ^{5}}) = ln (1) - ln (x^{5} y^{5})

= ln (1) - ln (x^{5} y^{5})

Apply log rule:

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

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

= ln (1) - (ln (x^{5}) + ln (y^{5}))

Apply log rule:

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

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

= ln (1) - (5 ln (x) + ln (y^{5}))

Apply log rule:

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

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

= ln (1) - (5 ln (x) + 5 ln (y))

Apply log rule:

lo g_{a} (1) = 0

= 0 - (5 ln (x) + 5 ln (y))

0 - (5 ln (x) + 5 ln (y)) = - (5 ln (x) + 5 ln (y))

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

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ln (\frac{1}{x ^{5}})

Frequently Asked Questions (FAQ)

What is ln(1/(x^5y^5)) ?
The solution to ln(1/(x^5y^5)) is -(5ln(x)+5ln(y))