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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

3 ln (v + 1) = ln ((v + 1)^{3})

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

ln (3.436 - 1) - ln (1.718)

2 ln (3 x^{2}) + 8

ln (2) - \frac{1}{3} ln (5)

ln (\frac{sin ( x )}{e ^{x}})

ln (\frac{x y + x}{x ^{2} + y ^{2}})

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