What is ln(a)-5ln(b)+3ln(c) ?

The solution to ln(a)-5ln(b)+3ln(c) is ln((ac^3)/(b^5))

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simplify ln(a)-5ln(b)+3ln(c)

simplify

ln (a) - 5 ln (b) + 3 ln (c)

ln (\frac{a c ^{3}}{b ^{5}})

Solution steps

ln (a) - 5 ln (b) + 3 ln (c)

Apply log rule:

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

5 ln (b) = ln (b^{5})

= ln (a) - ln (b^{5}) + 3 ln (c)

Apply log rule:

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

ln (a) - ln (b^{5}) = ln (\frac{a}{b ^{5}})

= ln (\frac{a}{b ^{5}}) + 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 ^{5}}) + ln (c^{3})

Apply log rule:

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

ln (\frac{a}{b ^{5}}) + ln (c^{3}) = ln (c^{3} \frac{a}{b ^{5}})

= ln (c^{3} \frac{a}{b ^{5}})

Multiply fractions:

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

= ln (\frac{a c ^{3}}{b ^{5}})

ln (\frac{2 3}{3})

6 ln (x - 5) - ln (x^{2} - 8 x + 15) + 2 ln (x - 3)

2 ln (x - 3) - ln (6) - 3 ln (x + 2)

\frac{1}{2} ln ∣ x - 2 ∣ + \frac{1}{2} ln ∣ x + 2 ∣

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

What is ln(a)-5ln(b)+3ln(c) ?
The solution to ln(a)-5ln(b)+3ln(c) is ln((ac^3)/(b^5))