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Popular >

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

Solution

simplify

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

Solution

2 y - ln (2)

Solution steps

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

Apply log rule:

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

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

= ln (e^{2 y}) - ln (2)

Apply log rule:

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

ln (e^{2 y}) = 2 y ln (e)

= 2 y ln (e) - ln (2)

2 y ln (e) = 2 y

= 2 y - ln (2)

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Frequently Asked Questions (FAQ)

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