What is ln(x)+2ln(x+2)+3ln(x-1) ?

The solution to ln(x)+2ln(x+2)+3ln(x-1) is ln(x(x+2)^2(x-1)^3)

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

3 ln (x - 1) = ln ((x - 1)^{3})

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

Apply log rule:

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

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

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

0.5 ln (\frac{9}{7})

\frac{ln ( 60 ) - ln ( 37.8 )}{0.98}

lo g_{2} (\frac{1}{( 1 - p ) ^{n}})

lo g_{x} (0.37) - lo g_{x} (0.73)

- 3 ln (y) + ln (\frac{3 x + 3 y}{y})

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