Question

solve the logarithmic equation for x. if there are no answers, enter none. \\(\log_{11}(4) + \log_{11}(x) = 1\\)

Explanation:

Step1: Apply log addition rule

Using the property \(\log_b(a) + \log_b(c)=\log_b(ac)\), we get \(\log_{11}(4x)=1\).

Step2: Convert to exponential form

Recall that \(\log_b(y)=k\) implies \(b^k = y\). So, \(11^1 = 4x\).

Step3: Solve for x

Simplify \(11 = 4x\), then \(x=\frac{11}{4}\). Check domain: \(x>0\) and \(4x>0\), so \(x = \frac{11}{4}\) is valid.

Answer:

\(\frac{11}{4}\)