What is log_{8}(1/(8p)) ?

The solution to log_{8}(1/(8p)) is -log_{8}(p)-1

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simplify log_{8}(1/(8p))

simplify

lo g_{8} (\frac{1}{8 p})

- lo g_{8} (p) - 1

Solution steps

lo g_{8} (\frac{1}{8 p})

Apply log rule:

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

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

= lo g_{8} (1) - lo g_{8} (8 p)

Apply log rule:

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

lo g_{8} (8 p) = lo g_{8} (8) + lo g_{8} (p)

= lo g_{8} (1) - (lo g_{8} (p) + lo g_{8} (8))

Apply log rule:

lo g_{a} (1) = 0

= 0 - (lo g_{8} (p) + lo g_{8} (8))

Apply log rule:

lo g_{a} (a) = 1

= 0 - (lo g_{8} (p) + 1)

0 - (1 + lo g_{8} (p)) = - (1 + lo g_{8} (p))

= - (lo g_{8} (p) + 1)

Distribute parentheses

= - (lo g_{8} (p)) - (1)

Apply minus-plus rules

+ (- a) = - a

= - lo g_{8} (p) - 1

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