What is simplify-log_{2}(3/8) ?

The solution to simplify-log_{2}(3/8) is -log_{2}(3)+3

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simplify-log_{2}(3/8)

simplify

- lo g_{2} (\frac{3}{8})

- lo g_{2} (3) + 3

Decimal Notation

1.41503 \dots

Solution steps

- lo g_{2} (\frac{3}{8})

Apply log rule:

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

- lo g_{2} (\frac{3}{8}) = - (lo g_{2} (3) - lo g_{2} (8))

= - (lo g_{2} (3) - lo g_{2} (8))

lo g_{2} (8) = 3

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

Apply the distributive law:

- (a - b) = - a + b

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

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

- lo g_{10} (5.4 \cdot 1 0^{- 4})

ln (2 + e^{1}) - ln (2 + e^{- 3})

3 ln (2) + 5 ln (x) - \frac{1}{2} ln (x + 6)

3 ln (2) + 5 ln (x) - \frac{1}{2} ln (x + 3)

What is simplify-log_{2}(3/8) ?
The solution to simplify-log_{2}(3/8) is -log_{2}(3)+3