What is log_{4}(16k^8x) ?

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

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simplify log_{4}(16k^8x)

simplify

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

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

Solution steps

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

Factor the number:

16 = 4^{2}

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

lo g_{4} (k^{8} x) : 8 lo g_{4} (k) + lo g_{4} (x)

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

Apply rule:

a + (b + c) = a + b + c

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

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

5 lo g_{2} (x) - 3 lo g_{2} (y)

lo g_{b} (\frac{x ^{4}}{z ^{2}})

2 (ln (x) - ln (x + 1) - ln (x - 1))

2 ln (x) + 3 ln (x + 1)

ln (e (x - 8))

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