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Popular >

simplify ln(2*2^{1/5})

Solution

simplify

ln (2 \cdot 2^{\frac{1}{5}})

Solution

\frac{6}{5} ln (2)

+1

Decimal Notation

0.83177 \dots

Solution steps

ln (2 \cdot 2^{\frac{1}{5}})

Apply log rule:

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

ln (2 \cdot 2^{\frac{1}{5}}) = ln (2) + ln (2^{\frac{1}{5}})

= ln (2) + ln (2^{\frac{1}{5}})

Apply log rule:

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

ln (2^{\frac{1}{5}}) = \frac{1}{5} ln (2)

= ln (2) + \frac{1}{5} ln (2)

Factor out common term

ln (2)

= ln (2) (1 + \frac{1}{5})

1 + \frac{1}{5} = \frac{6}{5}

= \frac{6}{5} ln (2)

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Frequently Asked Questions (FAQ)

What is ln(2*2^{1/5}) ?
The solution to ln(2*2^{1/5}) is 6/5 ln(2)