Question

Solve question 3 for 41 points

Answer 1

Answer:

(2)

Step-by-step explanation:

Our logarithmic expression is: $ln(\frac{\sqrt{e} }{y^3} )$.

Remember the logarithmic property that ln(a/b) = lna - lnb. So, we can write this as:

$ln(\frac{\sqrt{e} }{y^3} )=ln(\sqrt{e} )-ln(y^3)$

Also, we can write square roots as powers of one-half, so √e = $e^{1/2}$. There's another log property that: $ln(a^b)=b*ln(a)$. We can apply that here for both the √e and the y³:

$ln(\sqrt{e} )-ln(y^3)=\frac{1}{2} ln(e)-3ln(y)$

Finally, note that ln(e) is just 1, so we have:

$\frac{1}{2} ln(e)-3ln(y)=\frac{1}{2} -3ln(y)=\frac{1-6ln(y)}{2}$

The answer is thus (2).

~ an aesthetics lover