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

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

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

join

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

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

Decimal Notation

- 0.12618 \dots

Solution steps

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

Apply log rule:

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

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

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

3^{5} = 243

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

ln (x^{5}) - ln (x^{3})

- 5 [lo g_{10} (x) - lo g_{10} (y - 2)]

4 lo g_{3} (x) + lo g_{3} (7)

ln (413.93) - ln (280)

lo g_{5} (x + 6) + 2 lo g_{5} (x)

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