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Popular >

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

Solution

simplify

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

Solution

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (y z^{3}) = ln (y) + ln (z^{3})

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

Apply log rule:

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

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

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

- (ln (y) + 3 ln (z)) : - ln (y) - 3 ln (z)

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

Popular Examples

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Frequently Asked Questions (FAQ)

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