Solve \(log_{4}\)(y − 9) + \(log_{4}\)(3) = \(log_{4}\)(81).

We will use the properties of the logarithm to solve the equation.

Answer: The solution of the given equation is y = 36.

Let us see how we will use the properties of the logarithm to solve the equation.

Explanation:

It is given that, \(log_{4}\)(y − 9) + \(log_{4}\)(3) = \(log_{4}\)(81).

We will use the formula log a + log b = log ab.

\(log_{4}\) (3 × ( y - 9 )) = \(log_{4}\)(81)           

3 × ( y - 9 ) = 81

y - 9 = 27 

y = 36

Hence, the value of y is 36.