What is 1/8 ln(3)-1/8 ln(8) ?

The solution to 1/8 ln(3)-1/8 ln(8) is 1/8 ln(3/8)

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

simplify

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

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

Decimal Notation

- 0.12260 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

Combine same powers :

Rewrite as

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

lo g_{5} (3) - lo g_{5} (t)

lo g_{e} (2 x)

lo g_{10} (\frac{a}{b ^{2} c})

lo g_{10} (x^{2} - 5 x - 14) - lo g_{10} (x^{2} - 4)

2 lo g_{b} (3) + lo g_{b} (2)

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