Question

solve the following logarithmic equation. be sure to reject any value of x that is not in the domain of the original logarithmic expression. give the exact answer.\\(\log_{7}x = 2\\)\
solve the equation. select the correct choice below and, if necessary, fill in the answer box to complete your choice.\
a. the solution set is \\(\\{\\ \\}\\). (simplify your answer.)\
b. there are infinitely many solutions.\
c. there is no solution.

Explanation:

Step1: Recall logarithm definition

The logarithmic equation \(\log_{b}a = c\) is equivalent to \(b^{c}=a\) (where \(b>0,b
eq1,a>0\)). For \(\log_{7}x = 2\), we use this definition.

Step2: Convert to exponential form

Applying the definition, we get \(x = 7^{2}\).

Step3: Calculate \(7^{2}\)

\(7^{2}=7\times7 = 49\). Also, check the domain: since \(x = 49>0\), it is in the domain of the logarithmic function \(\log_{7}x\).

Answer:

A. The solution set is \(\{49\}\)