What is 1/2 log_{2}(7)-2log_{2}(6) ?

The solution to 1/2 log_{2}(7)-2log_{2}(6) is log_{2}((sqrt(7))/9)-2

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simplify 1/2 log_{2}(7)-2log_{2}(6)

simplify

\frac{1}{2} lo g_{2} (7) - 2 lo g_{2} (6)

lo g_{2} (\frac{7}{9}) - 2

Decimal Notation

- 3.76624 \dots

Solution steps

\frac{1}{2} lo g_{2} (7) - 2 lo g_{2} (6)

2 lo g_{2} (6) = 2 + 2 lo g_{2} (3)

= \frac{1}{2} lo g_{2} (7) - (2 + 2 lo g_{2} (3))

Apply the distributive law:

- (a + b) = - a - b

- (2 + 2 lo g_{2} (3)) = - 2 - 2 lo g_{2} (3)

= \frac{1}{2} lo g_{2} (7) - 2 - 2 lo g_{2} (3)

\frac{1}{2} lo g_{2} (7) = lo g_{2} (7^{\frac{1}{2}})

- 2 lo g_{2} (3) = - lo g_{2} (3^{2})

= lo g_{2} (7^{\frac{1}{2}}) - 2 - lo g_{2} (3^{2})

lo g_{2} (7^{\frac{1}{2}}) - lo g_{2} (3^{2}) = lo g_{2} (\frac{7 ^{\frac{1}{2}}}{9})

= lo g_{2} (\frac{7 ^{\frac{1}{2}}}{9}) - 2

Apply exponent rule:

a^{\frac{1}{2}} = a

7^{\frac{1}{2}} = 7

= lo g_{2} (\frac{7}{9}) - 2

\frac{1}{3} lo g_{2} (y) - lo g_{2} (x) - lo g_{2} (x + 2)

ln (\frac{74}{130})

lo g_{3} (\frac{x ^{2} - 14 x + 24}{4}) - 5 x + 2

2 ln (x) + 7 ln (y) - 3 ln (z)

ln (3) + 2 ln (x)

What is 1/2 log_{2}(7)-2log_{2}(6) ?
The solution to 1/2 log_{2}(7)-2log_{2}(6) is log_{2}((sqrt(7))/9)-2