What is simplify-6/5 ln(2)-1/5 ln(3) ?

The solution to simplify-6/5 ln(2)-1/5 ln(3) is -ln(2\sqrt[5]{6})

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simplify-6/5 ln(2)-1/5 ln(3)

simplify

- \frac{6}{5} ln (2) - \frac{1}{5} ln (3)

Decimal Notation

- 1.05149 \dots

Solution steps

- \frac{6}{5} ln (2) - \frac{1}{5} ln (3)

Apply log rule:

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

\frac{6}{5} ln (2) = ln (2^{\frac{6}{5}})

= - ln (2^{\frac{6}{5}}) - \frac{1}{5} ln (3)

Apply log rule:

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

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

= - ln (2^{\frac{6}{5}}) - ln (3^{\frac{1}{5}})

Rewrite

- ln (2^{\frac{6}{5}}) - ln (3^{\frac{1}{5}})

- (ln (2^{\frac{6}{5}}) + ln (3^{\frac{1}{5}}))

= - (ln (2^{\frac{6}{5}}) + ln (3^{\frac{1}{5}}))

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (2^{\frac{6}{5}}) + ln (3^{\frac{1}{5}}) = ln (2^{\frac{6}{5}} \cdot 3^{\frac{1}{5}})

= - ln (2^{\frac{6}{5}} \cdot 3^{\frac{1}{5}})

ln (\frac{25}{80})

\frac{25.5 \cdot 38}{292 \cdot 1 0 ^{- 3} \cdot 8} ln (\frac{780}{450})

\frac{1}{2} ln (43 + 8) - \frac{1}{2} ln (4)

\frac{7 ln ( 101 )}{2} + 534

ln (1.25 x)

What is simplify-6/5 ln(2)-1/5 ln(3) ?
The solution to simplify-6/5 ln(2)-1/5 ln(3) is -ln(2\sqrt[5]{6})