What is join (5ln(2))/(ln(5/4)) ?

The solution to join (5ln(2))/(ln(5/4)) is (ln(32))/(ln(5/4))

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join (5ln(2))/(ln(5/4))

join

\frac{5 ln ( 2 )}{ln ( \frac{5}{4} )}

\frac{ln ( 32 )}{ln ( \frac{5}{4} )}

Decimal Notation

15.53141 \dots

Solution steps

\frac{5 ln ( 2 )}{ln ( \frac{5}{4} )}

Apply log rule:

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

5 ln (2) = ln (2^{5})

= \frac{ln ( 2 ^{5} )}{ln ( \frac{5}{4} )}

2^{5} = 32

= \frac{ln ( 32 )}{ln ( \frac{5}{4} )}

lo g_{10} (an t i lo g_{4} (lo g_{2} (20) - 1))

\frac{1}{2} lo g_{3} (2)

(x - y ln (y) + y ln (x)) d x + x (ln (y) - ln (x))

lo g_{10} (\frac{y ^{2} x}{3 z})

4 lo g_{10} (x) - \frac{1}{4} lo g_{10} (x^{2} + 1) + 3 lo g_{10} (x - 1)

What is join (5ln(2))/(ln(5/4)) ?
The solution to join (5ln(2))/(ln(5/4)) is (ln(32))/(ln(5/4))