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Popular >

simplify-ln(x*e^y)

Solution

simplify

- ln (x \cdot e^{y})

Solution

- ln (x) - y

Solution steps

- ln (x e^{y})

Apply log rule:

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

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

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

Apply log rule:

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

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

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

y ln (e) = y

= - (y + ln (x))

Distribute parentheses

= - (ln (x)) - (y)

Apply minus-plus rules

+ (- a) = - a

= - ln (x) - y

Popular Examples

simplify 0.46+(0.025963)/2 ln((0.0155)/(3.5))simplify

0.46 + \frac{0.025963}{2} ln (\frac{0.0155}{3.5})

join 15/4 ln(2)join

\frac{15}{4} ln (2)

simplify 6ln(7)-9ln(8)simplify

6 ln (7) - 9 ln (8)

simplify ln((e^x)/2)simplify

ln (\frac{e ^{x}}{2})

simplify ln(10/1000000)simplify

ln (\frac{10}{1000000})

Frequently Asked Questions (FAQ)

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