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Popular >

simplify ln(3)+1/3 ln(64)

Solution

simplify

ln (3) + \frac{1}{3} ln (64)

Solution

ln (12)

+1

Decimal Notation

2.48490 \dots

Solution steps

ln (3) + \frac{1}{3} ln (64)

Apply log rule:

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

\frac{1}{3} ln (64) = ln (6 4^{\frac{1}{3}})

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

Apply log rule:

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

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

= ln (3 \cdot 6 4^{\frac{1}{3}})

3 \cdot 6 4^{\frac{1}{3}} = 12

= ln (12)

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Frequently Asked Questions (FAQ)

What is ln(3)+1/3 ln(64) ?
The solution to ln(3)+1/3 ln(64) is ln(12)