What is log_{2}(2 1/4) ?

The solution to log_{2}(2 1/4) is 2log_{2}(3)-2

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simplify log_{2}(2 1/4)

simplify

lo g_{2} (2 \frac{1}{4})

2 lo g_{2} (3) - 2

Decimal Notation

1.16992 \dots

Solution steps

lo g_{2} (2 \frac{1}{4})

Convert mixed numbers to improper fractions:

2 \frac{1}{4} = \frac{9}{4}

= lo g_{2} (\frac{9}{4})

Apply log rule:

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

lo g_{2} (\frac{9}{4}) = lo g_{2} (9) - lo g_{2} (4)

= lo g_{2} (9) - lo g_{2} (4)

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

lo g_{2} (4) = 2

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

f (2 x)

\frac{x ^{2}}{- x}

\frac{\frac{x ^{2} - 4}{x - 3}}{\frac{x ^{2} + 7 x - 18}{x + 9}}

(x + 2 y)^{4}