What is (a/b)-2ln(a^3)+4ln(b) ?

The solution to (a/b)-2ln(a^3)+4ln(b) is a/b+ln((b^4)/(a^6))

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simplify (a/b)-2ln(a^3)+4ln(b)

simplify

(\frac{a}{b}) - 2 ln (a^{3}) + 4 ln (b)

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

Solution steps

(\frac{a}{b}) - 2 ln (a^{3}) + 4 ln (b)

Apply log rule:

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

2 ln (a^{3}) = ln ((a^{3})^{2})

= (\frac{a}{b}) - ln ((a^{3})^{2}) + 4 ln (b)

Apply log rule:

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

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

= (\frac{a}{b}) - ln ((a^{3})^{2}) + ln (b^{4})

Apply log rule:

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

ln (b^{4}) - ln ((a^{3})^{2}) = ln (\frac{b ^{4}}{( a ^{3} ) ^{2}})

= \frac{a}{b} + ln (\frac{b ^{4}}{( a ^{3} ) ^{2}})

(a^{3})^{2} = a^{6}

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

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

ln (\frac{5}{1000})

lo g_{b} (\frac{x ^{3} \cdot y}{z ^{3}})

5 lo g_{4} (x) + 9 lo g_{4} (y)

ln ∣ 7 ∣ - ln ∣ 4 ∣

What is (a/b)-2ln(a^3)+4ln(b) ?
The solution to (a/b)-2ln(a^3)+4ln(b) is a/b+ln((b^4)/(a^6))