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Popular >

simplify 1/2 ln(8)-ln(3sqrt(2))

Solution

simplify

\frac{1}{2} ln (8) - ln (32)

Solution

ln (\frac{2}{3})

+1

Decimal Notation

- 0.40546 \dots

Solution steps

\frac{1}{2} ln (8) - ln (32)

Apply log rule:

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

\frac{1}{2} ln (8) = ln (8^{\frac{1}{2}})

= ln (8^{\frac{1}{2}}) - ln (32)

Apply log rule:

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

ln (8^{\frac{1}{2}}) - ln (32) = ln (\frac{8 ^{\frac{1}{2}}}{3 2})

= ln (\frac{8 ^{\frac{1}{2}}}{3 2})

\frac{8 ^{\frac{1}{2}}}{3 2} = \frac{2}{3}

= ln (\frac{2}{3})

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Frequently Asked Questions (FAQ)

What is 1/2 ln(8)-ln(3sqrt(2)) ?
The solution to 1/2 ln(8)-ln(3sqrt(2)) is ln(2/3)