What is ln(a)-6ln(b)+4ln(c) ?

The solution to ln(a)-6ln(b)+4ln(c) is ln((ac^4)/(b^6))

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simplify ln(a)-6ln(b)+4ln(c)

simplify

ln (a) - 6 ln (b) + 4 ln (c)

ln (\frac{a c ^{4}}{b ^{6}})

Solution steps

ln (a) - 6 ln (b) + 4 ln (c)

Apply log rule:

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

6 ln (b) = ln (b^{6})

= ln (a) - ln (b^{6}) + 4 ln (c)

Apply log rule:

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

ln (a) - ln (b^{6}) = ln (\frac{a}{b ^{6}})

= ln (\frac{a}{b ^{6}}) + 4 ln (c)

Apply log rule:

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

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

= ln (\frac{a}{b ^{6}}) + ln (c^{4})

Apply log rule:

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

ln (\frac{a}{b ^{6}}) + ln (c^{4}) = ln (c^{4} \frac{a}{b ^{6}})

= ln (c^{4} \frac{a}{b ^{6}})

Multiply fractions:

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

= ln (\frac{a c ^{4}}{b ^{6}})

ln (2 x) + ln (4 y)

ln (2 π \frac{l}{g})

2 lo g_{10} (x + 3) - lo g_{10} (x - 2)

12 ln (x) + 5 ln (y) - 11 ln (z)

ln (\frac{x + 4}{x ^{2} - 5 x + 6})

What is ln(a)-6ln(b)+4ln(c) ?
The solution to ln(a)-6ln(b)+4ln(c) is ln((ac^4)/(b^6))