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Popular >

simplify 1/4 ln(2)-1/8 ln(4/3)

Solution

simplify

\frac{1}{4} ln (2) - \frac{1}{8} ln (\frac{4}{3})

Solution

\frac{1}{8} ln (3)

+1

Decimal Notation

0.13732 \dots

Solution steps

\frac{1}{4} ln (2) - \frac{1}{8} ln (\frac{4}{3})

Apply log rule:

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

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

= ln (2^{\frac{1}{4}}) - \frac{1}{8} ln (\frac{4}{3})

Apply log rule:

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

\frac{1}{8} ln (\frac{4}{3}) = ln ((\frac{4}{3})^{\frac{1}{8}})

= ln (2^{\frac{1}{4}}) - ln ((\frac{4}{3})^{\frac{1}{8}})

Apply log rule:

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

ln (2^{\frac{1}{4}}) - ln ((\frac{4}{3})^{\frac{1}{8}}) = ln \frac{2 ^{\frac{1}{4}}}{( \frac{4}{3} ) ^{\frac{1}{8}}}

= ln \frac{2 ^{\frac{1}{4}}}{( \frac{4}{3} ) ^{\frac{1}{8}}}

Rewrite as

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

Apply log rule

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

assuming

x \geq 0

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

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Frequently Asked Questions (FAQ)

What is 1/4 ln(2)-1/8 ln(4/3) ?
The solution to 1/4 ln(2)-1/8 ln(4/3) is 1/8 ln(3)