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Popular >

simplify log_{4}(16x^8)

Solution

simplify

lo g_{4} (16 x^{8})

Solution

2 + 8 lo g_{4} (x)

Solution steps

lo g_{4} (16 x^{8})

Factor the number:

16 = 4^{2}

= lo g_{4} (4^{2} x^{8})

Apply log rule:

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

lo g_{4} (4^{2} x^{8}) = lo g_{4} (4^{2}) + lo g_{4} (x^{8})

= lo g_{4} (4^{2}) + lo g_{4} (x^{8})

Apply log rule:

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

lo g_{4} (4^{2}) = 2

= 2 + lo g_{4} (x^{8})

Apply log rule

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

lo g_{4} (x^{8}) = 8 lo g_{4} (x)

= 2 + 8 lo g_{4} (x)

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Frequently Asked Questions (FAQ)

What is log_{4}(16x^8) ?
The solution to log_{4}(16x^8) is 2+8log_{4}(x)