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Popular >

simplify 1/6 ln(8)-1/6 ln(4)

Solution

simplify

\frac{1}{6} ln (8) - \frac{1}{6} ln (4)

Solution

\frac{1}{6} ln (2)

+1

Decimal Notation

0.11552 \dots

Solution steps

\frac{1}{6} ln (8) - \frac{1}{6} ln (4)

Apply log rule:

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

\frac{1}{6} ln (8) = ln (8^{\frac{1}{6}})

= ln (8^{\frac{1}{6}}) - \frac{1}{6} ln (4)

Apply log rule:

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

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

= ln (8^{\frac{1}{6}}) - ln (4^{\frac{1}{6}})

Apply log rule:

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

ln (8^{\frac{1}{6}}) - ln (4^{\frac{1}{6}}) = ln (\frac{8 ^{\frac{1}{6}}}{4 ^{\frac{1}{6}}})

= ln (\frac{8 ^{\frac{1}{6}}}{4 ^{\frac{1}{6}}})

Rewrite as

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

Apply log rule

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

assuming

x \geq 0

= \frac{1}{6} ln (2)

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Frequently Asked Questions (FAQ)

What is 1/6 ln(8)-1/6 ln(4) ?
The solution to 1/6 ln(8)-1/6 ln(4) is 1/6 ln(2)