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Popular >

simplify log_{b}(a^5b^4)

Solution

simplify

lo g_{b} (a^{5} b^{4})

Solution

5 lo g_{b} (a) + 4

Solution steps

lo g_{b} (a^{5} b^{4})

Apply log rule:

lo g_{a} (x y) = lo g_{a} (x) + lo g_{a} (y)

lo g_{b} (a^{5} b^{4}) = lo g_{b} (a^{5}) + lo g_{b} (b^{4})

= lo g_{b} (a^{5}) + lo g_{b} (b^{4})

Apply log rule

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x), assuming x > 0

lo g_{b} (a^{5}) = 5 lo g_{b} (a)

= 5 lo g_{b} (a) + lo g_{b} (b^{4})

Apply log rule:

lo g_{a} (a^{b}) = b

lo g_{b} (b^{4}) = 4

= 5 lo g_{b} (a) + 4

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Frequently Asked Questions (FAQ)

What is log_{b}(a^5b^4) ?
The solution to log_{b}(a^5b^4) is 5log_{b}(a)+4