What is 2ln(x-3)+ln(x+2)-6ln(x) ?

The solution to 2ln(x-3)+ln(x+2)-6ln(x) is ln(((x-3)^2(x+2))/(x^6))

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simplify 2ln(x-3)+ln(x+2)-6ln(x)

simplify

2 ln (x - 3) + ln (x + 2) - 6 ln (x)

ln (\frac{( x - 3 ) ^{2} ( x + 2 )}{x ^{6}})

Solution steps

2 ln (x - 3) + ln (x + 2) - 6 ln (x)

Apply log rule:

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

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

= ln ((x - 3)^{2}) + ln (x + 2) - 6 ln (x)

Apply log rule:

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

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

= ln ((x - 3)^{2} (x + 2)) - 6 ln (x)

Apply log rule:

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

6 ln (x) = ln (x^{6})

= ln ((x - 3)^{2} (x + 2)) - ln (x^{6})

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

ln ((x - 3)^{2} (x + 2)) - ln (x^{6}) = ln (\frac{( x - 3 ) ^{2} ( x + 2 )}{x ^{6}})

= ln (\frac{( x - 3 ) ^{2} ( x + 2 )}{x ^{6}})

lo g_{3} (a^{10})

2 lo g_{10} (x) + lo g_{10} (x + 1) - 1

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

ln (1.5 a e^{b t})

lo g_{10} (x (x - 1)^{2})

What is 2ln(x-3)+ln(x+2)-6ln(x) ?
The solution to 2ln(x-3)+ln(x+2)-6ln(x) is ln(((x-3)^2(x+2))/(x^6))