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Popular >

simplify log_{4}(64x^5)

Solution

simplify

lo g_{4} (64 x^{5})

Solution

3 + 5 lo g_{4} (x)

Solution steps

lo g_{4} (64 x^{5})

Factor the number:

64 = 4^{3}

= lo g_{4} (4^{3} x^{5})

Apply log rule:

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

lo g_{4} (4^{3} x^{5}) = lo g_{4} (4^{3}) + lo g_{4} (x^{5})

= lo g_{4} (4^{3}) + lo g_{4} (x^{5})

Apply log rule:

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

lo g_{4} (4^{3}) = 3

= 3 + lo g_{4} (x^{5})

Apply log rule

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

lo g_{4} (x^{5}) = 5 lo g_{4} (x)

= 3 + 5 lo g_{4} (x)

Popular Examples

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expand ln(((m^5)/(n^2))^3)expand

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lo g_{2} (3 x y^{2})

Frequently Asked Questions (FAQ)

What is log_{4}(64x^5) ?
The solution to log_{4}(64x^5) is 3+5log_{4}(x)