What is ln(3)+2/3 ln(16/10) ?

The solution to ln(3)+2/3 ln(16/10) is ln((12\sqrt[3]{5})/5)

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simplify ln(3)+2/3 ln(16/10)

simplify

ln (3) + \frac{2}{3} ln (\frac{16}{10})

Decimal Notation

1.41194 \dots

Solution steps

ln (3) + \frac{2}{3} ln (\frac{16}{10})

Apply log rule:

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

\frac{2}{3} ln (\frac{16}{10}) = ln ((\frac{16}{10})^{\frac{2}{3}})

= ln (3) + ln ((\frac{16}{10})^{\frac{2}{3}})

Apply log rule:

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

ln (3) + ln ((\frac{16}{10})^{\frac{2}{3}}) = ln (3 (\frac{16}{10})^{\frac{2}{3}})

= ln (3 (\frac{16}{10})^{\frac{2}{3}})

ln^{3} (\frac{1 + x}{1 - e ^{2 x}})

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

ln (\frac{125}{16}) - ln (2)

\frac{1}{24} ln (cos (3) x^{2}) + c

lo g_{a} (x^{3}) - lo g_{a} (x^{4}) + 2 lo g_{a} (x)

What is ln(3)+2/3 ln(16/10) ?
The solution to ln(3)+2/3 ln(16/10) is ln((12\sqrt[3]{5})/5)