What is (ln(11)+ln(4)-ln(2))/(ln(4)-ln(11)) ?

The solution to (ln(11)+ln(4)-ln(2))/(ln(4)-ln(11)) is (ln(22))/(ln(4/11))

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simplify (ln(11)+ln(4)-ln(2))/(ln(4)-ln(11))

simplify

\frac{ln ( 11 ) + ln ( 4 ) - ln ( 2 )}{ln ( 4 ) - ln ( 11 )}

\frac{ln ( 22 )}{ln ( \frac{4}{11} )}

Decimal Notation

- 3.05559 \dots

Solution steps

\frac{ln ( 11 ) + ln ( 4 ) - ln ( 2 )}{ln ( 4 ) - ln ( 11 )}

Apply log rule:

lo g_{c} (a) + lo g_{c} (b) = lo g_{c} (ab)

ln (11) + ln (4) = ln (11 \cdot 4)

= \frac{ln ( 11 \cdot 4 ) - ln ( 2 )}{ln ( 4 ) - ln ( 11 )}

Multiply the numbers:

11 \cdot 4 = 44

= \frac{ln ( 44 ) - ln ( 2 )}{ln ( 4 ) - ln ( 11 )}

Apply log rule:

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

ln (44) - ln (2) = ln (\frac{44}{2})

= \frac{ln ( \frac{44}{2} )}{ln ( 4 ) - ln ( 11 )}

Divide the numbers:

\frac{44}{2} = 22

= \frac{ln ( 22 )}{ln ( 4 ) - ln ( 11 )}

Apply log rule:

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

ln (4) - ln (11) = ln (\frac{4}{11})

= \frac{ln ( 22 )}{ln ( \frac{4}{11} )}

lo g_{10} (8) + lo g_{10} (x) - 2 lo g_{10} (x + 4)

lo g_{10} (2 x) + lo g_{10} (50 y)

lo g_{2} (x y)

lo g_{6} (\frac{c}{36})

lo g_{10} (\frac{x ( x + 6 )}{( x + 5 ) ^{6}})

What is (ln(11)+ln(4)-ln(2))/(ln(4)-ln(11)) ?
The solution to (ln(11)+ln(4)-ln(2))/(ln(4)-ln(11)) is (ln(22))/(ln(4/11))