What is 1/2 [ln(x-4)+5ln(x^2+4x)] ?

The solution to 1/2 [ln(x-4)+5ln(x^2+4x)] is 1/2 ln((x-4)(x^2+4x)^5)

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simplify 1/2 [ln(x-4)+5ln(x^2+4x)]

simplify

\frac{1}{2} [ln (x - 4) + 5 ln (x^{2} + 4 x)]

\frac{1}{2} ln ((x - 4) (x^{2} + 4 x)^{5})

Solution steps

\frac{1}{2} [ln (x - 4) + 5 ln (x^{2} + 4 x)]

Apply log rule:

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

5 ln (x^{2} + 4 x) = ln ((x^{2} + 4 x)^{5})

= \frac{1}{2} [ln (x - 4) + ln ((x^{2} + 4 x)^{5})]

Apply log rule:

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

ln (x - 4) + ln ((x^{2} + 4 x)^{5}) = ln ((x - 4) (x^{2} + 4 x)^{5})

= \frac{1}{2} [ln ((x - 4) (x^{2} + 4 x)^{5})]

Remove parentheses:

(a) = a

= \frac{1}{2} ln ((x - 4) (x^{2} + 4 x)^{5})

lo g_{10} (2 x) + lo g_{10} (8 x)

lo g_{10} (\frac{y}{z ^{9}})

- lo g_{10} (8 \cdot 1 0^{- 8})

lo g_{10} (\frac{1 0 ^{x}}{x ( x ^{2} + 1 ) ( x ^{4} + 2 )})

5 ln (x) + 2 ln (y)

What is 1/2 [ln(x-4)+5ln(x^2+4x)] ?
The solution to 1/2 [ln(x-4)+5ln(x^2+4x)] is 1/2 ln((x-4)(x^2+4x)^5)