Logx logy=log(x y),y can be expressed as ?
**Solution:**
To find the expression for 'y' in terms of 'x' from the equation log(x) + log(y) = log(xy), we can use the properties of logarithms.
**1. Using the Product Rule:**
The product rule states that log(a) + log(b) = log(ab). Applying this rule to the equation log(x) + log(y) = log(xy), we get:
log(x) + log(y) = log(xy)
Therefore, we can rewrite the equation as:
log(xy) = log(xy)
**2. Applying the Inverse Property:**
The inverse property of logarithms states that log(base a) a = 1. Therefore, applying the inverse property to the equation log(xy) = log(xy), we get:
xy = xy
**3. Solving for 'y':**
Since xy = xy, we can conclude that the equation is true for all values of 'x' and 'y'.
Therefore, 'y' can be expressed as any value, as long as 'x' is not equal to zero. This is because the logarithm function is undefined for the base zero.
In summary, the equation log(x) + log(y) = log(xy) implies that 'y' can be any value as long as 'x' is not equal to zero.
Logx logy=log(x y),y can be expressed as ?
Log x+log y = log (x+y)
log xy = log (x+y)
xy= x+y
y = x/x-1