What is simplify-3ln(a)+2ln(b) ?

The solution to simplify-3ln(a)+2ln(b) is ln((b^2)/(a^3))

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simplify-3ln(a)+2ln(b)

simplify

- 3 ln (a) + 2 ln (b)

ln (\frac{b ^{2}}{a ^{3}})

Solution steps

- 3 ln (a) + 2 ln (b)

Apply log rule:

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

3 ln (a) = ln (a^{3})

= - ln (a^{3}) + 2 ln (b)

Apply log rule:

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

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

= - ln (a^{3}) + ln (b^{2})

Apply log rule:

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

ln (b^{2}) - ln (a^{3}) = ln (\frac{b ^{2}}{a ^{3}})

= ln (\frac{b ^{2}}{a ^{3}})

lo g_{3} (x - 2) + lo g_{3} (x - 4)

- ln (\frac{35}{2})

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

ln (1.08893 x^{0.037})

What is simplify-3ln(a)+2ln(b) ?
The solution to simplify-3ln(a)+2ln(b) is ln((b^2)/(a^3))