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 + 3) = 2\\) \
rewrite the given equation without logarithms. do not solve for x. \
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 \\(\boxed{}\\). (type an integer or a simplified fraction.) \
b. there are infinitely many solutions. \
c. there is no solution.

Explanation:

Step1: Rewrite using logarithm definition

Recall that if $\log_b a = c$, then $b^c = a$. For $\log_7(x + 3)=2$, we apply this definition. So, $7^2 = x + 3$.

Step2: Solve for x

Calculate $7^2 = 49$. Then the equation becomes $49 = x + 3$. Subtract 3 from both sides: $x = 49 - 3 = 46$.

Step3: Check domain

The argument of the logarithm $x + 3$ must be positive. For $x = 46$, $46 + 3 = 49>0$, so it's in the domain.

Answer:

The solution set is $\{46\}$ (so the correct choice is A with the solution 46).