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Popular >

simplify 3/2 ln(x^6)-3/4 ln(x^8)

Solution

simplify

\frac{3}{2} ln (x^{6}) - \frac{3}{4} ln (x^{8})

Solution

ln (x^{3})

Solution steps

\frac{3}{2} ln (x^{6}) - \frac{3}{4} ln (x^{8})

Apply log rule:

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

\frac{3}{2} ln (x^{6}) = ln ((x^{6})^{\frac{3}{2}})

= ln ((x^{6})^{\frac{3}{2}}) - \frac{3}{4} ln (x^{8})

Apply log rule:

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

\frac{3}{4} ln (x^{8}) = ln ((x^{8})^{\frac{3}{4}})

= ln ((x^{6})^{\frac{3}{2}}) - ln ((x^{8})^{\frac{3}{4}})

Apply log rule:

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

ln ((x^{6})^{\frac{3}{2}}) - ln ((x^{8})^{\frac{3}{4}}) = ln \frac{( x ^{6} ) ^{\frac{3}{2}}}{( x ^{8} ) ^{\frac{3}{4}}}

= ln \frac{( x ^{6} ) ^{\frac{3}{2}}}{( x ^{8} ) ^{\frac{3}{4}}}

Simplify

\frac{( x ^{6} ) ^{\frac{3}{2}}}{( x ^{8} ) ^{\frac{3}{4}}} : x^{3}

= ln (x^{3})

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Frequently Asked Questions (FAQ)

What is 3/2 ln(x^6)-3/4 ln(x^8) ?
The solution to 3/2 ln(x^6)-3/4 ln(x^8) is ln(x^3)