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

The solution to (ln(5))/(2ln(2)-ln(5)) is (ln(5))/(ln(4/5))

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simplify (ln(5))/(2ln(2)-ln(5))

simplify

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

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

Decimal Notation

- 7.21256 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

lo g_{c} (a) - lo g_{c} (b) = lo g_{c} (\frac{a}{b})

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

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

2^{2} = 4

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

ln (x y) + 7 ln (\frac{y}{z}) - 5 ln (x yz)

lo g_{4} (3.188 - 1) + lo g_{4} (2 \cdot 3.188 - 5)

ln (\frac{e ^{2} x ^{2} - 3}{x ( x + 1 ) ^{5}})

\frac{1}{3} ln (x) + \frac{1}{4} ln (y) + c

2 ln (e) + 2 lo g_{x} (+ 3 lo g_{y} (x))

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