Understand given logarithmic equation: Understand the given logarithmic equation. We are given the equation y = log_2(x + 2) + 2, where log_2 denotes the logarithm base 2. We need to solve for x.Isolate logarithmic term: Isolate the logarithmic term. To solve for x, we first need to isolate the logarithmic term. We can do this by subtracting 2 from both sides of the equation. y - 2 = log_2(x + 2)Convert to exponential equation: Convert the logarithmic equation to an exponential equation. The inverse of a logarithm is an exponentiation. We can rewrite the equation in exponential form using the definition of a logarithm: if log_b(a) = c, then b^c = a. 2^(y - 2) = x + 2Isolate x: Isolate x. Now we need to isolate x by subtracting 2 from both sides of the equation. 2^(y - 2) - 2 = x

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$y=\log _{2}(x+2)+2$

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Precalculus

Quotient property of logarithms

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y=\log _{2}(x+2)+2

Understand given logarithmic equation: Understand the given logarithmic equation. $\newline$ We are given the equation $y = \log_2(x + 2) + 2$ , where $\log_2$ denotes the logarithm base $2$ . We need to solve for $x$ .
Isolate logarithmic term: Isolate the logarithmic term. $\newline$ To solve for $x$ , we first need to isolate the logarithmic term. We can do this by subtracting $2$ from both sides of the equation. $\newline$ $y - 2 = \log_2(x + 2)$
Convert to exponential equation: Convert the logarithmic equation to an exponential equation. $\newline$ The inverse of a logarithm is an exponentiation. We can rewrite the equation in exponential form using the definition of a logarithm: if $\log_b(a) = c$ , then $b^c = a$ . $\newline$ $2^{y - 2} = x + 2$
Isolate x: Isolate $x$ . Now we need to isolate $x$ by subtracting $2$ from both sides of the equation. $2^{(y - 2)} - 2 = x$