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Popular >

simplify 1/3 (ln(x)-2ln(y))

Solution

simplify

\frac{1}{3} (ln (x) - 2 ln (y))

Solution

\frac{1}{3} ln (\frac{x}{y ^{2}})

Solution steps

\frac{1}{3} (ln (x) - 2 ln (y))

Apply log rule:

a lo g_{c} (b) = lo g_{c} (b^{a})

2 ln (y) = ln (y^{2})

= \frac{1}{3} (ln (x) - ln (y^{2}))

Apply log rule:

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

ln (x) - ln (y^{2}) = ln (\frac{x}{y ^{2}})

= \frac{1}{3} ln (\frac{x}{y ^{2}})

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2 ln (8) + 2 ln (y)

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- 2 lo g_{10} (x + 1) + lo g_{10} (x) + lo g_{10} (x^{2} - 1)

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lo g_{3} (\frac{x}{27})

Frequently Asked Questions (FAQ)

What is 1/3 (ln(x)-2ln(y)) ?
The solution to 1/3 (ln(x)-2ln(y)) is 1/3 ln(x/(y^2))