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

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

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

simplify

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

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

Decimal Notation

- 6.21256 \dots

Solution steps

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

2^{2} = 4

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

3 ln (x + 2) - ln (x - 1)

ln (\frac{4}{x}) + ln (\frac{2}{x ^{3}})

lo g_{a} (\frac{( x - 5 ) ^{6}}{( x + 7 ) ^{7}})

5.24 - lo g_{10} (\frac{0.022}{0.1})

ln (18) - ln (3)

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