What is ln(6)-3ln(a)+ln(b) ?

The solution to ln(6)-3ln(a)+ln(b) is ln((6b)/(a^3))

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simplify ln(6)-3ln(a)+ln(b)

simplify

ln (6) - 3 ln (a) + ln (b)

ln (\frac{6 b}{a ^{3}})

Solution steps

ln (6) - 3 ln (a) + ln (b)

Apply log rule:

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

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

= ln (6) - ln (a^{3}) + ln (b)

Apply log rule:

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

ln (6) - ln (a^{3}) = ln (\frac{6}{a ^{3}})

= ln (\frac{6}{a ^{3}}) + ln (b)

Apply log rule:

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

ln (\frac{6}{a ^{3}}) + ln (b) = ln (b \frac{6}{a ^{3}})

= ln (b \frac{6}{a ^{3}})

Multiply fractions:

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

= ln (\frac{6 b}{a ^{3}})

u^{2} + 2 u - 4 ln (u) + 2 ln (y)

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

ln (x + 1) + ln (k)

ln (X) + ln (Y) - 3 ln (Z)

ln (a \cdot e^{- \frac{b}{x}})

What is ln(6)-3ln(a)+ln(b) ?
The solution to ln(6)-3ln(a)+ln(b) is ln((6b)/(a^3))