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_{2}(x + 2) = 4\\) 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: Convert log to exponential form

Recall that if $\log_{b}a = c$, then $b^{c}=a$. For $\log_{2}(x + 2)=4$, we have $2^{4}=x + 2$.

Step2: Calculate $2^{4}$ and solve for x

Calculate $2^{4}=16$. So the equation becomes $16=x + 2$. Subtract 2 from both sides: $x=16 - 2=14$.

Step3: Check domain

The argument of the logarithm $x + 2$ must be positive. For $x = 14$, $14+2 = 16>0$, so it is in the domain.

Answer:

A. The solution set is $\{14\}$