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

The solution to 2ln(a^3b^4)-3ln(a)-3ln(ab^2) is ln(b^2)

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simplify 2ln(a^3b^4)-3ln(a)-3ln(ab^2)

simplify

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

ln (b^{2})

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Simplify

\frac{( a ^{3} b ^{4} ) ^{2}}{a ^{3}} : a^{3} b^{8}

= ln (a^{3} b^{8}) - 3 ln (a b^{2})

Apply log rule:

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

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

= ln (a^{3} b^{8}) - ln ((a b^{2})^{3})

Apply log rule:

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

ln (a^{3} b^{8}) - ln ((a b^{2})^{3}) = ln (\frac{a ^{3} b ^{8}}{( a b ^{2} ) ^{3}})

= ln (\frac{a ^{3} b ^{8}}{( a b ^{2} ) ^{3}})

Simplify

\frac{a ^{3} b ^{8}}{( a b ^{2} ) ^{3}} : b^{2}

= ln (b^{2})

ln (\frac{5}{14})

\frac{( - \frac{1}{2} ln ( x ) - \frac{1}{4} ln ( 2 + x ^{2} ) )}{e}

20 \cdot lo g_{10} (\frac{4 \cdot π \cdot 30 \cdot 1 0 ^{3}}{\frac{300}{175}})

\frac{1}{4} ln (10 + 101)

ln (\frac{1}{2 π} \cdot e^{- \frac{( x - y ) ^{2}}{2}})

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