What is (3ln(7/4))/(ln(7)-2ln(2))-2 ?

The solution to (3ln(7/4))/(ln(7)-2ln(2))-2 is 1

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simplify (3ln(7/4))/(ln(7)-2ln(2))-2

simplify

\frac{3 ln ( \frac{7}{4} )}{ln ( 7 ) - 2 ln ( 2 )} - 2

1

Solution steps

\frac{3 ln ( \frac{7}{4} )}{ln ( 7 ) - 2 ln ( 2 )} - 2

Apply log rule:

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

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

= \frac{3 ln ( \frac{7}{4} )}{ln ( 7 ) - ln ( 2 ^{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{3 ln ( \frac{7}{4} )}{ln ( \frac{7}{2 ^{2}} )} - 2

2^{2} = 4

= \frac{3 ln ( \frac{7}{4} )}{ln ( \frac{7}{4} )} - 2

Cancel

\frac{3 ln ( \frac{7}{4} )}{ln ( \frac{7}{4} )} : 3

= 3 - 2

Simplify

= 1

lo g_{5} (14 x + 15) - lo g_{5} (\frac{1}{14 x - 15})

ln (x^{10} 2 - x)

lo g_{5} (x) - 8 lo g_{5} (y) - 9 lo g_{5} (z)

lo g_{10} (x^{3} y^{6})

lo g_{10} (30) + lo g_{10} (5)

What is (3ln(7/4))/(ln(7)-2ln(2))-2 ?
The solution to (3ln(7/4))/(ln(7)-2ln(2))-2 is 1