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Popular >

simplify ln(1/(ex))

Solution

simplify

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

Solution

- ln (x) - 1

Solution steps

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

Apply log rule:

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

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

= ln (1) - ln (e x)

Apply log rule:

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

ln (e x) = ln (e) + ln (x)

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

Apply log rule:

lo g_{a} (1) = 0

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

Apply log rule:

lo g_{a} (a) = 1

= 0 - (ln (x) + 1)

0 - (1 + ln (x)) = - (1 + ln (x))

= - (ln (x) + 1)

Distribute parentheses

= - (ln (x)) - (1)

Apply minus-plus rules

+ (- a) = - a

= - ln (x) - 1

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Frequently Asked Questions (FAQ)

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