What is (2ln(4))/(ln(12)-ln(4)) ?

The solution to (2ln(4))/(ln(12)-ln(4)) is (4ln(2))/(ln(3))

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simplify (2ln(4))/(ln(12)-ln(4))

simplify

\frac{2 ln ( 4 )}{ln ( 12 ) - ln ( 4 )}

\frac{4 ln ( 2 )}{ln ( 3 )}

Solution steps

\frac{2 ln ( 4 )}{ln ( 12 ) - ln ( 4 )}

Apply log rule:

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

ln (12) - ln (4) = ln (\frac{12}{4})

= \frac{2 ln ( 4 )}{ln ( \frac{12}{4} )}

Divide the numbers:

\frac{12}{4} = 3

= \frac{2 ln ( 4 )}{ln ( 3 )}

Simplify

ln (4) : 2 ln (2)

= \frac{2 \cdot 2 ln ( 2 )}{ln ( 3 )}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{4 ln ( 2 )}{ln ( 3 )}

- ln (c) + ln (c + x)

ln (87) - ln (22)

- lo g_{10} (8.4 \cdot 1 0^{- 6})

\frac{ln ( 10 ) - ln ( 8 )}{( 8 - 6 )}

ln (\frac{0.365}{1.10325})

What is (2ln(4))/(ln(12)-ln(4)) ?
The solution to (2ln(4))/(ln(12)-ln(4)) is (4ln(2))/(ln(3))