What is (7ln(7)+4ln(2))/(ln(7)-2ln(2)) ?

The solution to (7ln(7)+4ln(2))/(ln(7)-2ln(2)) is (7ln(7)+4ln(2))/(ln(7/4))

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simplify (7ln(7)+4ln(2))/(ln(7)-2ln(2))

simplify

\frac{7 ln ( 7 ) + 4 ln ( 2 )}{ln ( 7 ) - 2 ln ( 2 )}

\frac{7 ln ( 7 ) + 4 ln ( 2 )}{ln ( \frac{7}{4} )}

Decimal Notation

29.29502 \dots

Solution steps

\frac{7 ln ( 7 ) + 4 ln ( 2 )}{ln ( 7 ) - 2 ln ( 2 )}

Apply log rule:

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

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

= \frac{7 ln ( 7 ) + 4 ln ( 2 )}{ln ( 7 ) - ln ( 2 ^{2} )}

Apply log rule:

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

ln (7) - ln (2^{2}) = ln (\frac{7}{2 ^{2}})

= \frac{7 ln ( 7 ) + 4 ln ( 2 )}{ln ( \frac{7}{2 ^{2}} )}

2^{2} = 4

= \frac{7 ln ( 7 ) + 4 ln ( 2 )}{ln ( \frac{7}{4} )}

5 lo g_{2} (m) + 4 lo g_{2} (n)

lo g_{10} (125) + lo g_{10} (25) + lo g_{10} (5)

2 lo g_{10} (4) + 2 lo g_{10} (x)

ln (\frac{x}{x + 2})

5 lo g_{10} (4) - 4 lo g_{10} (x)

What is (7ln(7)+4ln(2))/(ln(7)-2ln(2)) ?
The solution to (7ln(7)+4ln(2))/(ln(7)-2ln(2)) is (7ln(7)+4ln(2))/(ln(7/4))