Question

Write 3 + 2 log z - log(x² + 2x + 1) +1/2 log y as a single logarithm with coefficient 1.​

Answer 1

Answer:

$\displaystyle \log\frac{1000z^2y^{\frac{1}{2}}}{(x+1)^2}$ OR $\displaystyle 3+\log\frac{z^2y^{\frac{1}{2}}}{(x+1)^2}$

Choose the more appropriate answer

Step-by-step explanation:

I read your problem as $3+2\log z-\log(x^2+2x+1)+\frac{1}{2}\log y$:

$\displaystyle 3+2\log z-\log(x^2+2x+1)+\frac{1}{2}\log y\\\\\log1000+\log z^2-\log(x+1)^2+\log y^{\frac{1}{2}}\\\\\log1000z^2-\log(x+1)^2+\log y^{\frac{1}{2}}\\\\\log\frac{1000z^2}{(x+1)^2}+\log y^{\frac{1}{2}}\\\\\log\frac{1000z^2y^{\frac{1}{2}}}{(x+1)^2}$