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Popular >

simplify 1/3 ln(a^2b^4)

Solution

simplify

\frac{1}{3} ln (a^{2} b^{4})

Solution

\frac{2}{3} ln (a) + \frac{4}{3} ln (b)

Solution steps

\frac{1}{3} ln (a^{2} b^{4})

Apply log rule:

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

\frac{1}{3} ln (a^{2} b^{4}) = \frac{1}{3} ln (a^{2}) + \frac{1}{3} ln (b^{4})

= \frac{1}{3} ln (a^{2}) + \frac{1}{3} ln (b^{4})

Apply log rule:

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

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

= \frac{1}{3} \cdot 2 ln (a) + \frac{1}{3} ln (b^{4})

Apply log rule:

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

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

= \frac{1}{3} \cdot 2 ln (a) + \frac{1}{3} \cdot 4 ln (b)

\frac{1}{3} \cdot 2 ln (a) = \frac{2}{3} ln (a)

\frac{1}{3} \cdot 4 ln (b) = \frac{4}{3} ln (b)

= \frac{2}{3} ln (a) + \frac{4}{3} ln (b)

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Frequently Asked Questions (FAQ)

What is 1/3 ln(a^2b^4) ?
The solution to 1/3 ln(a^2b^4) is 2/3 ln(a)+4/3 ln(b)