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Popular >

simplify 2log_{e}(ab^2)

Solution

simplify

2 lo g_{e} (a b^{2})

Solution

2 ln (a) + 4 ln (b)

Solution steps

2 lo g_{e} (a b^{2})

Apply log rule:

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

2 lo g_{e} (a b^{2}) = 2 lo g_{e} (a) + 2 lo g_{e} (b^{2})

= 2 lo g_{e} (a) + 2 lo g_{e} (b^{2})

Apply log rule:

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

lo g_{e} (b^{2}) = 2 lo g_{e} (b)

= 2 lo g_{e} (a) + 2 \cdot 2 lo g_{e} (b)

2 lo g_{e} (a) = 2 ln (a)

2 \cdot 2 lo g_{e} (b) = 4 ln (b)

= 2 ln (a) + 4 ln (b)

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Frequently Asked Questions (FAQ)

What is 2log_{e}(ab^2) ?
The solution to 2log_{e}(ab^2) is 2ln(a)+4ln(b)