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

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

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

simplify

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

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

Decimal Notation

7.21256 \dots

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

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

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

2^{2} = 4

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

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