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

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

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

simplify

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

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

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (c^{2}) - ln (d^{3}) = ln (\frac{c ^{2}}{d ^{3}})

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

Apply log rule:

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

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

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

Multiply fractions:

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

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

ln (\frac{306.34}{1173.15})

e^{2 (l n (x) - l n (1 - x))}

ln (\frac{86 - 60}{86 - 50})

ln (x^{4} (1 - x)^{14})

ln (\frac{5 e ^{4 x + 3}}{3 x + 2})

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