What is ln(a)-4ln(b)+5ln(c) ?

The solution to ln(a)-4ln(b)+5ln(c) is ln((ac^5)/(b^4))

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simplify ln(a)-4ln(b)+5ln(c)

simplify

ln (a) - 4 ln (b) + 5 ln (c)

ln (\frac{a c ^{5}}{b ^{4}})

Solution steps

ln (a) - 4 ln (b) + 5 ln (c)

Apply log rule:

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

4 ln (b) = ln (b^{4})

= ln (a) - ln (b^{4}) + 5 ln (c)

Apply log rule:

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

ln (a) - ln (b^{4}) = ln (\frac{a}{b ^{4}})

= ln (\frac{a}{b ^{4}}) + 5 ln (c)

Apply log rule:

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

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

= ln (\frac{a}{b ^{4}}) + ln (c^{5})

Apply log rule:

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

ln (\frac{a}{b ^{4}}) + ln (c^{5}) = ln (c^{5} \frac{a}{b ^{4}})

= ln (c^{5} \frac{a}{b ^{4}})

Multiply fractions:

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

= ln (\frac{a c ^{5}}{b ^{4}})

ln (n + 1) + ln (n - 1)

\frac{ln ( 2.01 ) - ln ( 2 )}{2.01 - 2}

ln (θ^{n} \cdot x^{θ - 1})

4 ln (x) + 6 ln (y)

ln (\frac{0.01}{1})

What is ln(a)-4ln(b)+5ln(c) ?
The solution to ln(a)-4ln(b)+5ln(c) is ln((ac^5)/(b^4))