What is simplify-2ln(a)+1/3 ln(b)-3ln(c) ?

The solution to simplify-2ln(a)+1/3 ln(b)-3ln(c) is ln((b^{1/3})/(a^2c^3))

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simplify-2ln(a)+1/3 ln(b)-3ln(c)

simplify

- 2 ln (a) + \frac{1}{3} ln (b) - 3 ln (c)

ln (\frac{b ^{\frac{1}{3}}}{a ^{2} c ^{3}})

Solution steps

- 2 ln (a) + \frac{1}{3} ln (b) - 3 ln (c)

Apply log rule:

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

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

= - ln (a^{2}) + \frac{1}{3} ln (b) - 3 ln (c)

Apply log rule:

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

\frac{1}{3} ln (b) = ln (b^{\frac{1}{3}})

= - ln (a^{2}) + ln (b^{\frac{1}{3}}) - 3 ln (c)

Apply log rule:

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

ln (b^{\frac{1}{3}}) - ln (a^{2}) = ln (\frac{b ^{\frac{1}{3}}}{a ^{2}})

= ln (\frac{b ^{\frac{1}{3}}}{a ^{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{b ^{\frac{1}{3}}}{a ^{2}}) - ln (c^{3})

Apply log rule:

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

ln (\frac{b ^{\frac{1}{3}}}{a ^{2}}) - ln (c^{3}) = ln \frac{\frac{b ^{\frac{1}{3}}}{a ^{2}}}{c ^{3}}

= ln \frac{\frac{b ^{\frac{1}{3}}}{a ^{2}}}{c ^{3}}

Apply the fraction rule:

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

= ln (\frac{b ^{\frac{1}{3}}}{a ^{2} c ^{3}})

\frac{1}{3} [ln (x + 3) + 2 ln (x^{3} + 2 x)]

\frac{ln ( 4.1 ) - ln ( 3.9 )}{4 \cdot 0.1}

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

ln (\frac{10}{620.9 9 ^{2}})

\frac{9}{2} ln (2)

What is simplify-2ln(a)+1/3 ln(b)-3ln(c) ?
The solution to simplify-2ln(a)+1/3 ln(b)-3ln(c) is ln((b^{1/3})/(a^2c^3))