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Popular >

simplify ln(2e^{x/y})

Solution

simplify

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

Solution

ln (2) + \frac{x}{y}

Solution steps

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

Apply log rule:

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

ln (2 e^{\frac{x}{y}}) = ln (2) + ln (e^{\frac{x}{y}})

= ln (2) + ln (e^{\frac{x}{y}})

Apply log rule:

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

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

= ln (2) + \frac{x}{y} ln (e)

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

= ln (2) + \frac{x}{y}

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Frequently Asked Questions (FAQ)

What is ln(2e^{x/y}) ?
The solution to ln(2e^{x/y}) is ln(2)+x/y