Question

solve. simplify your answer.\\(\log_{36} y + \log_{36} 2 = \frac{1}{2}\\)\\(y = \boxed{}\\)

Explanation:

Step1: Use log addition rule

Using the property of logarithms \(\log_a M+\log_a N = \log_a(MN)\), we can combine the left - hand side of the equation \(\log_{36}y+\log_{36}2=\frac{1}{2}\) into \(\log_{36}(2y)=\frac{1}{2}\)

Step2: Convert to exponential form

Recall that if \(\log_a b = c\), then \(b = a^c\). For the equation \(\log_{36}(2y)=\frac{1}{2}\), we can rewrite it in exponential form. Here, \(a = 36\), \(b=2y\) and \(c=\frac{1}{2}\). So we have \(2y=36^{\frac{1}{2}}\)

Step3: Simplify \(36^{\frac{1}{2}}\)

We know that \(36^{\frac{1}{2}}=\sqrt{36} = 6\). So the equation becomes \(2y = 6\)

Step4: Solve for y

Divide both sides of the equation \(2y=6\) by 2. We get \(y=\frac{6}{2}=3\)

Answer:

\(3\)