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Popular >

simplify 4ln(x)-1/5 ln(x^4)

Solution

simplify

4 ln (x) - \frac{1}{5} ln (x^{4})

Solution

ln (x^{\frac{16}{5}})

Solution steps

4 ln (x) - \frac{1}{5} ln (x^{4})

Apply log rule:

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

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

= ln (x^{4}) - \frac{1}{5} ln (x^{4})

Apply log rule:

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

\frac{1}{5} ln (x^{4}) = ln ((x^{4})^{\frac{1}{5}})

= ln (x^{4}) - ln ((x^{4})^{\frac{1}{5}})

Apply log rule:

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

ln (x^{4}) - ln ((x^{4})^{\frac{1}{5}}) = ln (\frac{x ^{4}}{( x ^{4} ) ^{\frac{1}{5}}})

= ln (\frac{x ^{4}}{( x ^{4} ) ^{\frac{1}{5}}})

Simplify

\frac{x ^{4}}{( x ^{4} ) ^{\frac{1}{5}}} : x^{\frac{16}{5}}

= ln (x^{\frac{16}{5}})

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Frequently Asked Questions (FAQ)

What is 4ln(x)-1/5 ln(x^4) ?
The solution to 4ln(x)-1/5 ln(x^4) is ln(x^{16/5})