What is ln(1/(25k)) ?

The solution to ln(1/(25k)) is -ln(k)-2ln(5)

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simplify ln(1/(25k))

simplify

ln (\frac{1}{25 k})

- ln (k) - 2 ln (5)

Solution steps

ln (\frac{1}{25 k})

Apply log rule:

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

ln (\frac{1}{25 k}) = ln (1) - ln (25 k)

= ln (1) - ln (25 k)

Apply log rule:

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

ln (25 k) = ln (25) + ln (k)

= ln (1) - (ln (k) + ln (25))

Apply log rule:

lo g_{a} (1) = 0

= 0 - (ln (k) + ln (25))

ln (25) = 2 ln (5)

= 0 - (ln (k) + 2 ln (5))

0 - (2 ln (5) + ln (k)) = - (2 ln (5) + ln (k))

= - (ln (k) + 2 ln (5))

Distribute parentheses

= - (ln (k)) - (2 ln (5))

Apply minus-plus rules

+ (- a) = - a

= - ln (k) - 2 ln (5)

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