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Popular >

simplify ln((z^4)/(y^5))

Solution

simplify

ln (\frac{z ^{4}}{y ^{5}})

Solution

4 ln (z) - 5 ln (y)

Solution steps

ln (\frac{z ^{4}}{y ^{5}})

Apply log rule:

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

ln (\frac{z ^{4}}{y ^{5}}) = ln (z^{4}) - ln (y^{5})

= ln (z^{4}) - ln (y^{5})

Apply log rule:

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

ln (z^{4}) = 4 ln (z)

= 4 ln (z) - ln (y^{5})

Apply log rule:

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

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

= 4 ln (z) - 5 ln (y)

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Frequently Asked Questions (FAQ)

What is ln((z^4)/(y^5)) ?
The solution to ln((z^4)/(y^5)) is 4ln(z)-5ln(y)