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Popular >

simplify ln(ab^{1/2})

Solution

simplify

ln (a b^{\frac{1}{2}})

Solution

ln (a) + \frac{1}{2} ln (b)

Solution steps

ln (a b^{\frac{1}{2}})

Apply log rule:

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

ln (a b^{\frac{1}{2}}) = ln (a) + ln (b^{\frac{1}{2}})

= ln (a) + ln (b^{\frac{1}{2}})

Apply log rule:

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

ln (b^{\frac{1}{2}}) = \frac{1}{2} ln (b)

= ln (a) + \frac{1}{2} ln (b)

Popular Examples

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Frequently Asked Questions (FAQ)

What is ln(ab^{1/2}) ?
The solution to ln(ab^{1/2}) is ln(a)+1/2 ln(b)