What is log_{2}(9/14) ?

The solution to log_{2}(9/14) is 2log_{2}(3)-1-log_{2}(7)

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simplify log_{2}(9/14)

simplify

lo g_{2} (\frac{9}{14})

2 lo g_{2} (3) - 1 - lo g_{2} (7)

Decimal Notation

- 0.63742 \dots

Solution steps

lo g_{2} (\frac{9}{14})

Apply log rule:

lo g_{a} (\frac{x}{y}) = lo g_{a} (x) - lo g_{a} (y)

lo g_{2} (\frac{9}{14}) = lo g_{2} (9) - lo g_{2} (14)

= lo g_{2} (9) - lo g_{2} (14)

lo g_{2} (9) = 2 lo g_{2} (3)

lo g_{2} (14) = 1 + lo g_{2} (7)

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

Apply the distributive law:

- (a + b) = - a - b

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

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

\frac{9}{2} \times 2

- 4 \times (- 5)

\frac{5}{15}

ln ((e^{3})^{\frac{1}{2}})

What is log_{2}(9/14) ?
The solution to log_{2}(9/14) is 2log_{2}(3)-1-log_{2}(7)