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Popular >

simplify 1/3 ln(x)+4ln(2)

Solution

simplify

\frac{1}{3} ln (x) + 4 ln (2)

Solution

ln (16 x^{\frac{1}{3}})

Solution steps

\frac{1}{3} ln (x) + 4 ln (2)

Apply log rule:

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

\frac{1}{3} ln (x) = ln (x^{\frac{1}{3}})

= ln (x^{\frac{1}{3}}) + 4 ln (2)

Apply log rule:

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

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

= ln (x^{\frac{1}{3}}) + ln (2^{4})

Apply log rule:

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

ln (x^{\frac{1}{3}}) + ln (2^{4}) = ln (2^{4} x^{\frac{1}{3}})

= ln (2^{4} x^{\frac{1}{3}})

2^{4} = 16

= ln (16 x^{\frac{1}{3}})

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Frequently Asked Questions (FAQ)

What is 1/3 ln(x)+4ln(2) ?
The solution to 1/3 ln(x)+4ln(2) is ln(16x^{1/3})