What is join (5ln(3))/(ln(2/3)) ?

The solution to join (5ln(3))/(ln(2/3)) is (ln(243))/(ln(2/3))

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join (5ln(3))/(ln(2/3))

join

\frac{5 ln ( 3 )}{ln ( \frac{2}{3} )}

\frac{ln ( 243 )}{ln ( \frac{2}{3} )}

Decimal Notation

- 13.54755 \dots

Solution steps

\frac{5 ln ( 3 )}{ln ( \frac{2}{3} )}

Apply log rule:

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

5 ln (3) = ln (3^{5})

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

3^{5} = 243

= \frac{ln ( 243 )}{ln ( \frac{2}{3} )}

(2 \cdot 8.314) \cdot ln (\frac{1.5}{7})

- 5 ln (60 + \frac{5}{3} - 39) + 74.05 + 5 ln (\frac{5}{3})

- lo g_{10} (8.1 \cdot 1 0^{- 3})

ln (\frac{- 0.15415}{3})

- \frac{8.31 \cdot 310}{- 1 \cdot 9.65 \cdot 1 0 ^{4}} \cdot ln (\frac{160}{150})

What is join (5ln(3))/(ln(2/3)) ?
The solution to join (5ln(3))/(ln(2/3)) is (ln(243))/(ln(2/3))