What is log_{2}(x/(500)) ?

The solution to log_{2}(x/(500)) is log_{2}(x)-2-3log_{2}(5)

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simplify log_{2}(x/(500))

simplify

lo g_{2} (\frac{x}{500})

lo g_{2} (x) - 2 - 3 lo g_{2} (5)

Solution steps

lo g_{2} (\frac{x}{500})

Apply log rule:

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

lo g_{2} (\frac{x}{500}) = lo g_{2} (x) - lo g_{2} (500)

= lo g_{2} (x) - lo g_{2} (500)

lo g_{2} (500) = 2 + 3 lo g_{2} (5)

= lo g_{2} (x) - (2 + 3 lo g_{2} (5))

Apply the distributive law:

- (a + b) = - a - b

- (2 + 3 lo g_{2} (5)) = - 2 - 3 lo g_{2} (5)

= lo g_{2} (x) - 2 - 3 lo g_{2} (5)

ln (\frac{e ^{7}}{9})

4 lo g_{5} (x) + lo g_{5} (y)

ln (cos (x)) + ln (sin (x))

lo g_{10} (\frac{2 x ^{2}}{( y - 1 ) ^{3}})

- 0.66 \cdot lo g_{2} (0.66) - 0.33 lo g_{2} (0.33)

What is log_{2}(x/(500)) ?
The solution to log_{2}(x/(500)) is log_{2}(x)-2-3log_{2}(5)