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

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

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

simplify

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

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

Solution steps

ln (a) - (2 ln (b) - 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}) - ln (c))

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply the fraction rule:

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

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

ln (A e^{2})

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

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ln (\frac{1}{0.043})

ln (2) - ln (3) + ln (5)

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