What is 1/5 ln(3)-1/5 ln(8) ?

The solution to 1/5 ln(3)-1/5 ln(8) is 1/5 ln(3/8)

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simplify 1/5 ln(3)-1/5 ln(8)

simplify

\frac{1}{5} ln (3) - \frac{1}{5} ln (8)

\frac{1}{5} ln (\frac{3}{8})

Decimal Notation

- 0.19616 \dots

Solution steps

\frac{1}{5} ln (3) - \frac{1}{5} ln (8)

Apply log rule:

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

\frac{1}{5} ln (3) = ln (3^{\frac{1}{5}})

= ln (3^{\frac{1}{5}}) - \frac{1}{5} ln (8)

Apply log rule:

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

\frac{1}{5} ln (8) = ln (8^{\frac{1}{5}})

= ln (3^{\frac{1}{5}}) - ln (8^{\frac{1}{5}})

Apply log rule:

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

ln (3^{\frac{1}{5}}) - ln (8^{\frac{1}{5}}) = ln (\frac{3 ^{\frac{1}{5}}}{8 ^{\frac{1}{5}}})

= ln (\frac{3 ^{\frac{1}{5}}}{8 ^{\frac{1}{5}}})

Combine same powers :

Rewrite as

= ln ((\frac{3}{8})^{\frac{1}{5}})

Apply log rule

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

assuming

x \geq 0

= \frac{1}{5} ln (\frac{3}{8})

ln (\frac{x}{11})

lo g_{10} (x) + lo g_{10} (x^{2} - 25) - lo g_{10} (8) - lo g_{10} (x + 5)

lo g_{10} (\frac{z}{y ^{3} x ^{2}})

ln (2 x^{2}) + ln (5 x^{7})

lo g_{10} (y x^{3})

What is 1/5 ln(3)-1/5 ln(8) ?
The solution to 1/5 ln(3)-1/5 ln(8) is 1/5 ln(3/8)