What is join (ln(8/9))/(2ln(6)) ?

The solution to join (ln(8/9))/(2ln(6)) is (ln(8/9))/(ln(36))

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join (ln(8/9))/(2ln(6))

join

\frac{ln ( \frac{8}{9} )}{2 ln ( 6 )}

\frac{ln ( \frac{8}{9} )}{ln ( 36 )}

Decimal Notation

- 0.03286 \dots

Solution steps

\frac{ln ( \frac{8}{9} )}{2 ln ( 6 )}

Apply log rule:

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

2 ln (6) = ln (6^{2})

= \frac{ln ( \frac{8}{9} )}{ln ( 6 ^{2} )}

6^{2} = 36

= \frac{ln ( \frac{8}{9} )}{ln ( 36 )}

ln (x + 8) - ln (x - 8)

ln (e (x))

lo g_{10} (x^{2} + 2 x - 8) - lo g_{10} (x^{2} - 16)

- 6 lo g_{3} (x + 1) + 4 lo g_{3} (2 x)

ln (3) + ln (6) - ln (9)

What is join (ln(8/9))/(2ln(6)) ?
The solution to join (ln(8/9))/(2ln(6)) is (ln(8/9))/(ln(36))