Question

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

Answer 1

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

Choose the more appropriate answer

Explanation:

I read your problem as
`3+2\log z-\log(x^2+2x+1)+(1)/(2)\log y`:

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