What is (3*ln(4))/(8ln(4)-11ln(3)) ?

The solution to (3*ln(4))/(8ln(4)-11ln(3)) is (6ln(2))/(ln(65536/177147))

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simplify (3*ln(4))/(8ln(4)-11ln(3))

simplify

\frac{3 \cdot ln ( 4 )}{8 ln ( 4 ) - 11 ln ( 3 )}

\frac{6 ln ( 2 )}{ln ( \frac{65536}{177147} )}

Decimal Notation

- 4.18238 \dots

Solution steps

\frac{3 ln ( 4 )}{8 ln ( 4 ) - 11 ln ( 3 )}

Apply log rule:

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

8 ln (4) = ln (4^{8})

= \frac{3 ln ( 4 )}{ln ( 4 ^{8} ) - 11 ln ( 3 )}

Apply log rule:

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

11 ln (3) = ln (3^{11})

= \frac{3 ln ( 4 )}{ln ( 4 ^{8} ) - ln ( 3 ^{11} )}

Apply log rule:

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

ln (4^{8}) - ln (3^{11}) = ln (\frac{4 ^{8}}{3 ^{11}})

= \frac{3 ln ( 4 )}{ln ( \frac{4 ^{8}}{3 ^{11}} )}

\frac{4 ^{8}}{3 ^{11}} = \frac{65536}{177147}

= \frac{3 ln ( 4 )}{ln ( \frac{65536}{177147} )}

Simplify

ln (4) : 2 ln (2)

= \frac{3 \cdot 2 ln ( 2 )}{ln ( \frac{65536}{177147} )}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{6 ln ( 2 )}{ln ( \frac{65536}{177147} )}

lo g_{10} (\frac{18}{x})

ln (\frac{x x + 1}{2 e ^{4}})

lo g_{2} (x + 2) - lo g_{2} (x - 2)

lo g_{2} (\frac{x ^{3}}{x + 5})

- \frac{18 ln ( 2 )}{ln ( \frac{8}{5} )}

What is (3*ln(4))/(8ln(4)-11ln(3)) ?
The solution to (3*ln(4))/(8ln(4)-11ln(3)) is (6ln(2))/(ln(65536/177147))