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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

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

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

30 lo g_{16} (- 20 lo g_{16} (x))

lo g_{e} (2 e)

e^{18} + ln (16 x)

ln (500) - ln (250)

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