What is log_{2}(1/(8x)) ?

The solution to log_{2}(1/(8x)) is -log_{2}(x)-3

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simplify log_{2}(1/(8x))

simplify

lo g_{2} (\frac{1}{8 x})

- lo g_{2} (x) - 3

Solution steps

lo g_{2} (\frac{1}{8 x})

Apply log rule:

lo g_{c} (\frac{a}{b}) = lo g_{c} (a) - lo g_{c} (b)

lo g_{2} (\frac{1}{8 x}) = lo g_{2} (1) - lo g_{2} (8 x)

= lo g_{2} (1) - lo g_{2} (8 x)

Apply log rule:

lo g_{c} (ab) = lo g_{c} (a) + lo g_{c} (b)

lo g_{2} (8 x) = lo g_{2} (8) + lo g_{2} (x)

= lo g_{2} (1) - (lo g_{2} (x) + lo g_{2} (8))

Apply log rule:

lo g_{a} (1) = 0

= 0 - (lo g_{2} (x) + lo g_{2} (8))

lo g_{2} (8) = 3

= 0 - (lo g_{2} (x) + 3)

0 - (3 + lo g_{2} (x)) = - (3 + lo g_{2} (x))

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

Distribute parentheses

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

Apply minus-plus rules

+ (- a) = - a

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

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