Question

Solve for x.
log(x) = log(y + z) + log(y − z)

Answer 1

x = y² - z²

Explanation:

Data provided:

log(x) = log(y + z) + log(y − z) .................(1)

Now, from the properties of log

we know that

log(A) + log(B) = log(AB)

applying the above property on the equation given, we get

log(y + z) + log(y − z) = log( (y + z) × (y - z) )

or

log(y + z) + log(y − z) = log( y² - z² )

Substituting the above result in the equation 1 , we get

log(x) = log( y² - z² )

taking the anti-log both sides, we get

x = y² - z²