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Popular >

simplify-ln(3e^x)

Solution

simplify

- ln (3 e^{x})

Solution

- ln (3) - x

Solution steps

- ln (3 e^{x})

Apply log rule:

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

ln (3 e^{x}) = ln (3) + ln (e^{x})

= - (ln (e^{x}) + ln (3))

Apply log rule:

lo g_{a} (x^{b}) = b \cdot lo g_{a} (x)

ln (e^{x}) = x ln (e)

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

x ln (e) = x

= - (x + ln (3))

Distribute parentheses

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

Apply minus-plus rules

+ (- a) = - a

= - ln (3) - x

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Frequently Asked Questions (FAQ)

What is simplify-ln(3e^x) ?
The solution to simplify-ln(3e^x) is -ln(3)-x