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Popular >

simplify ln((x^3)/(2y))

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (x^{3}) = 3 ln (x)

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

Apply log rule:

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

ln (2 y) = ln (2) + ln (y)

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

- (ln (2) + ln (y)) : - ln (2) - ln (y)

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

Popular Examples

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Frequently Asked Questions (FAQ)

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