Question

If log x +log y = log(x+y), y can be expressed as

a) x-1 b)x c)x/x-1

Answer 1

$log(xy) = log(x + y ) \\ xy = x + y \\ xy - y = x \\ y(x - 1) = x \\ y = \frac{x}{x - 1}$

Answer 2

Answer:

Option c - $y=\frac{x}{x-1}$

Step-by-step explanation:

Given : Expression $\log x +\log y = \log(x+y)$

To find : y can be expressed as

Solution :

We apply logarithmic property in the given expression,

$\log x+\log y=\log(xy)$

Given expression -

$\log x +\log y = \log(x+y)$

$\log(xy)= \log(x+y)$

$xy= x+y$

$xy-y= x$

$y(x-1)= x$

$y=\frac{x}{(x-1)}$

Therefore, Option C is correct.