Question

What is 2logx−logy+2logz written as a single logarithm? log(xz)^2/y log2x/2yz logx^2y/z^2 logx^2/yz^2

Answer 1

Took the test, the answer is (xz)^2/y

Answer 2

Answer:
`\log(x^2z^2)/(y)`

Explanation:

Properties of logarithm:

`(i)\ \ n\log a = a^n\\\\ (ii)\ \ \log m +\log n =\log (mn)\\\\ (iii)\ \ \log m-\log n =\log(m)/(n)`

Consider,

`2\log x-\log y+2 \log z\\\\ =\log x^2-\log y+\log z^2\ \ \ \ \text{[By (i)]}\\\\= \log x^2+\log z^2-\log y\\\\=\log(x^2z^2)-\log y\ \ \ \ [\text{By } (ii) ]\\\\=\log((x^2z^2)/(y)) \ \ \ \ [\text{By (iii)}]`