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Popular >

simplify ln(4(e^{3x})^{1/6})

Solution

simplify

ln (4 (e^{3 x})^{\frac{1}{6}})

Solution

2 ln (2) + \frac{x}{2}

Solution steps

ln (4 (e^{3 x})^{\frac{1}{6}})

Apply log rule:

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

ln (4 (e^{3 x})^{\frac{1}{6}}) = ln (4) + ln ((e^{3 x})^{\frac{1}{6}})

= ln (4) + ln ((e^{3 x})^{\frac{1}{6}})

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln ((e^{3 x})^{\frac{1}{6}}) = \frac{1}{6} ln (e^{3 x})

= ln (4) + \frac{1}{6} ln (e^{3 x})

\frac{1}{6} ln (e^{3 x}) = \frac{x}{2}

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

ln (4) = 2 ln (2)

= 2 ln (2) + \frac{x}{2}

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Frequently Asked Questions (FAQ)

What is ln(4(e^{3x})^{1/6}) ?
The solution to ln(4(e^{3x})^{1/6}) is 2ln(2)+x/2