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Popular >

simplify ln(e^{y/x}y)

Solution

simplify

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

Solution

\frac{y}{x} + ln (y)

Solution steps

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

Apply log rule:

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

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

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

Apply log rule:

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

ln (e^{\frac{y}{x}}) = \frac{y}{x} ln (e)

= \frac{y}{x} ln (e) + ln (y)

\frac{y}{x} ln (e) = \frac{y}{x}

= \frac{y}{x} + ln (y)

Popular Examples

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Frequently Asked Questions (FAQ)

What is ln(e^{y/x}y) ?
The solution to ln(e^{y/x}y) is y/x+ln(y)