QuestionSolve for $x$ in the equation $\log _{9}(2+x)=\log _{16} 4-\log _{1} \sqrt{1-2 x}$ .

Studdy Solution

STEP 1

Assumptions1. The logarithmic equation given is $\log{9}(+x)=\log{16}4-\log{1} \sqrt{1- x}$ . . We are looking for the value of $x$ that satisfies this equation.
3. We assume that the logarithms are defined, which means $+x >0$ and $1-x >0$ .

STEP 2

First, we simplify the right side of the equation. Notice that $\log{16}4 =1/2$ because $16^{1/2} =4$ . And $\log{1} \sqrt{1-2 x}$ is undefined because the base of a logarithm cannot be1. Therefore, the original equation is incorrect.
$\log{9}(2+x)=\log{16}4-\log{1} \sqrt{1-2 x}$ $\log{9}(2+x)=1/2-\text{undefined}$ Since the equation contains an undefined term, it cannot be solved.

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