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

The solution to join (2ln(2))/(ln(2/3)) is (ln(4))/(ln(2/3))

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

join

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

\frac{ln ( 4 )}{ln ( \frac{2}{3} )}

Decimal Notation

- 3.41902 \dots

Solution steps

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

Apply log rule:

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

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

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

2^{2} = 4

= \frac{ln ( 4 )}{ln ( \frac{2}{3} )}

lo g_{3} (7) + lo g_{3} (12) - lo g_{3} (4)

ln (\frac{e ^{9}}{10})

(lo g_{b} (x) - lo g_{b} (y)) + 4 lo g_{b} (v)

lo g_{4} (\frac{16}{x + 5})

ln (\frac{535.6}{348.1})

What is join (2ln(2))/(ln(2/3)) ?
The solution to join (2ln(2))/(ln(2/3)) is (ln(4))/(ln(2/3))