Question

If T = 10x^2/y, then log T is equivalent to

(1 + 2log x) – log y
log(1 + 2x) – log y
(1 - 2log x) + log y
2(1 - log x) + log y

Answer 1

logT = 1 + 2log(x) - log(y)

Explanation:

Given
`T=(10x^(2) )/(y)`.

We need to evaluate
`logT`. Let us apply logarithm on both sides of the above equation.

`logT=log((10x^(2) )/(y))`

We know that
`log(ab)=log(a)+log(b)` and
`log((a)/(b))=log(a)-log(b)`,
`log(a^(b))=(b)log(a)`.

Hence,
`logT=log10+log(x^(2))-log(y)`

∴
`logT=1+2log(x)-log(y)`