What is ln((e^{sqrt(2y)})/c) ?

The solution to ln((e^{sqrt(2y)})/c) is sqrt(2)sqrt(y)-ln(c)

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

simplify

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

2 y - ln (c)

Solution steps

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

Apply log rule:

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

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

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

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 (c)

2 y ln (e) = 2 y

= 2 y - ln (c)

4 lo g_{a} (k) - 3 lo g_{a} (m)

- lo g_{10} (8.32 \cdot 1 0^{- 9})

2 ln (x e^{x})

6 ln (6) - 5 ln (5)

lo g_{10} (45) + lo g_{10} (2.5)

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