What is 1/3 [ln(x)+2ln(x+4)]-ln(x-1) ?

The solution to 1/3 [ln(x)+2ln(x+4)]-ln(x-1) is 1/3 ln(x(x+4)^2)-ln(x-1)

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simplify 1/3 [ln(x)+2ln(x+4)]-ln(x-1)

simplify

\frac{1}{3} [ln (x) + 2 ln (x + 4)] - ln (x - 1)

\frac{1}{3} ln (x (x + 4)^{2}) - ln (x - 1)

Solution steps

\frac{1}{3} [ln (x) + 2 ln (x + 4)] - ln (x - 1)

Apply log rule:

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

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

= \frac{1}{3} [ln (x) + ln ((x + 4)^{2})] - ln (x - 1)

Apply log rule:

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

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

= \frac{1}{3} [ln (x (x + 4)^{2})] - ln (x - 1)

Remove parentheses:

(a) = a

= \frac{1}{3} ln (x (x + 4)^{2}) - ln (x - 1)

4 [ln (z) + ln (z + 7)] - 2 ln (z - 7)

ln (x^{2}) - 2 ln (x)

- lo g_{10} (2.3 \cdot 1 0^{- 10})

3 lo g_{10} (x) - 2 lo g_{10} (x + 3)

- \frac{ln ( 2 ) - ln ( 3 )}{2} + 1

What is 1/3 [ln(x)+2ln(x+4)]-ln(x-1) ?
The solution to 1/3 [ln(x)+2ln(x+4)]-ln(x-1) is 1/3 ln(x(x+4)^2)-ln(x-1)