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Write the logarithmic equation in exponential form. $\newline$ $\log_{10}100 = 2$ $\newline$ $10^2 = \underline{\hspace{2em}}$

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Convert between exponential and logarithmic form: all bases

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Q. Write the logarithmic equation in exponential form.

\newline

\log_{10}100 = 2

\newline

10^2 = \underline{\hspace{2em}}

Identify base, logarithm result, and number: Identify the base (), the logarithm result (), and the number () from the logarithmic equation () = . In a logarithmic equation of the form _() = , is the base, is the number, and is the result. Here, the base is assumed to be because it is not specified (common logarithm), so = , = , and = .
Convert to exponential form: Convert the logarithmic equation to exponential form using the relationship $b^y = x$ . $\newline$ Substitute $b = 10$ , $y = 2$ , and $x = 100$ into the equation to get $10^2 = 100$ .
Check the calculation: Check the calculation to ensure that raising the base to the power of the result gives the number. $10^2 = 10 \times 10 = 100$ , which matches the number $x$ in the logarithmic equation.

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