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Popular >

simplify ln(1/(3x))

Solution

simplify

ln (\frac{1}{3 x})

Solution

- ln (x) - ln (3)

Solution steps

ln (\frac{1}{3 x})

Apply log rule:

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

ln (\frac{1}{3 x}) = ln (1) - ln (3 x)

= ln (1) - ln (3 x)

Apply log rule:

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

ln (3 x) = ln (3) + ln (x)

= ln (1) - (ln (x) + ln (3))

Apply log rule:

lo g_{a} (1) = 0

= 0 - (ln (x) + ln (3))

0 - (ln (3) + ln (x)) = - (ln (3) + ln (x))

= - (ln (x) + ln (3))

Distribute parentheses

= - (ln (x)) - (ln (3))

Apply minus-plus rules

+ (- a) = - a

= - ln (x) - ln (3)

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Frequently Asked Questions (FAQ)

What is ln(1/(3x)) ?
The solution to ln(1/(3x)) is -ln(x)-ln(3)