What is 8/5 ln(a)+9/10 ln(b) ?

The solution to 8/5 ln(a)+9/10 ln(b) is ln(a^{8/5}b^{9/10})

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simplify 8/5 ln(a)+9/10 ln(b)

simplify

\frac{8}{5} ln (a) + \frac{9}{10} ln (b)

ln (a^{\frac{8}{5}} b^{\frac{9}{10}})

Solution steps

\frac{8}{5} ln (a) + \frac{9}{10} ln (b)

Apply log rule:

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

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

= ln (a^{\frac{8}{5}}) + \frac{9}{10} ln (b)

Apply log rule:

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

\frac{9}{10} ln (b) = ln (b^{\frac{9}{10}})

= ln (a^{\frac{8}{5}}) + ln (b^{\frac{9}{10}})

Apply log rule:

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

ln (a^{\frac{8}{5}}) + ln (b^{\frac{9}{10}}) = ln (a^{\frac{8}{5}} b^{\frac{9}{10}})

= ln (a^{\frac{8}{5}} b^{\frac{9}{10}})

3 lo g_{6} (y - 3) - 4 lo g_{6} (y + 2)

lo g_{10} (2) \cdot \frac{1}{2}

ln (\frac{39}{40})

6 + 2 ln (6) - 2 ln (\frac{20}{3})

lo g_{10} (\frac{12.8}{5.76})

What is 8/5 ln(a)+9/10 ln(b) ?
The solution to 8/5 ln(a)+9/10 ln(b) is ln(a^{8/5}b^{9/10})