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log_(2)4=

$\log _{2} 4=$

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Convert between exponential and logarithmic form: all bases

Full solution

Q.

\log _{2} 4=

Identify variables: Identify $b$ , $x$ , and $y$ . $\newline$ Compare $\log_{2}4$ with $\log_{b}x = y$ . $\newline$ $b = 2$ $\newline$ $x = 4$ $\newline$ $y = ?$
Determine value of $y$ : Determine the value of $y$ that makes the equation true. $\newline$ Since $2^2 = 4$ , $y$ must be $2$ . $\newline$ Therefore, $\log_{2}4 = 2$ .
Convert to exponential form: Convert the logarithmic equation to exponential form. $\newline$ Substitute $b=2$ , $x=4$ , and $y=2$ in $b^y = x$ . $\newline$ Exponential equation: $2^2 = 4$ .

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