What is (ln(5/9)+2ln(13))/(6ln(13)) ?

The solution to (ln(5/9)+2ln(13))/(6ln(13)) is (ln(845/9))/(6ln(13))

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simplify (ln(5/9)+2ln(13))/(6ln(13))

simplify

\frac{ln ( \frac{5}{9} ) + 2 ln ( 13 )}{6 ln ( 13 )}

\frac{ln ( \frac{845}{9} )}{6 ln ( 13 )}

Decimal Notation

0.29513 \dots

Solution steps

\frac{ln ( \frac{5}{9} ) + 2 ln ( 13 )}{6 ln ( 13 )}

Apply log rule:

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

2 ln (13) = ln (1 3^{2})

= \frac{ln ( \frac{5}{9} ) + ln ( 1 3 ^{2} )}{6 ln ( 13 )}

Apply log rule:

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

ln (\frac{5}{9}) + ln (1 3^{2}) = ln (1 3^{2} \cdot \frac{5}{9})

= \frac{ln ( 1 3 ^{2} \cdot \frac{5}{9} )}{6 ln ( 13 )}

\frac{5}{9} \cdot 1 3^{2} = \frac{845}{9}

= \frac{ln ( \frac{845}{9} )}{6 ln ( 13 )}

lo g_{15} (\frac{x}{y})

lo g_{10} (P) - lo g_{10} (Q) - lo g_{10} (R)

ln (\frac{x + 2}{x - 2})

ln (f g)

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

What is (ln(5/9)+2ln(13))/(6ln(13)) ?
The solution to (ln(5/9)+2ln(13))/(6ln(13)) is (ln(845/9))/(6ln(13))