What is 2ln(x^4)-3ln(x^2)+4ln(x^3) ?

The solution to 2ln(x^4)-3ln(x^2)+4ln(x^3) is ln(x^{14})

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simplify 2ln(x^4)-3ln(x^2)+4ln(x^3)

simplify

2 ln (x^{4}) - 3 ln (x^{2}) + 4 ln (x^{3})

ln (x^{14})

Solution steps

2 ln (x^{4}) - 3 ln (x^{2}) + 4 ln (x^{3})

Apply log rule:

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

2 ln (x^{4}) = ln ((x^{4})^{2})

= ln ((x^{4})^{2}) - 3 ln (x^{2}) + 4 ln (x^{3})

Apply log rule:

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

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

= ln ((x^{4})^{2}) - ln ((x^{2})^{3}) + 4 ln (x^{3})

Apply log rule:

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

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

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

Simplify

\frac{( x ^{4} ) ^{2}}{( x ^{2} ) ^{3}} : x^{2}

= ln (x^{2}) + 4 ln (x^{3})

Apply log rule:

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

4 ln (x^{3}) = ln ((x^{3})^{4})

= ln (x^{2}) + ln ((x^{3})^{4})

Apply log rule:

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

ln (x^{2}) + ln ((x^{3})^{4}) = ln (x^{2} (x^{3})^{4})

= ln (x^{2} (x^{3})^{4})

Simplify

x^{2} (x^{3})^{4} : x^{14}

= ln (x^{14})

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What is 2ln(x^4)-3ln(x^2)+4ln(x^3) ?
The solution to 2ln(x^4)-3ln(x^2)+4ln(x^3) is ln(x^{14})