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ext{ exttt{log}}_{ $2$ }( $4$ )= $2$ \rightarrow $2$ ^{ $2$ }= $4$

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Convert between exponential and logarithmic form

Full solution

Q. ext{ exttt{log}}_{

2

}(

4

)=

2

\rightarrow

2

^{

2

}=

4

Given Logarithmic Equation: We are given the logarithmic equation $\log_{2}(4) = x$ , and we want to find the value of $x$ .
$\log_{2}(4) = x$
How can we rewrite this as an exponential equation?
$\log_{2}(4) = x$ can be rewritten as $2^{x} = 4$ .
Rewriting as Exponential: We have: $2^x = 4$ $\newline$ Can we express $4$ as a power of $2$ ? $\newline$ Yes, $4$ is $2$ squared, or $2^2$ . $\newline$ $2^x = 2^2$
Expressing $4$ as Power: The equation $2^x = 2^2$ suggests that the exponents must be equal since the bases are the same. $\newline$ Therefore, we can equate the exponents: $x = 2$ .
Equating Exponents: We have found that $x = 2$ . $\newline$ This means that $\log_{2} 4 = 2$ .

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