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# How do you write ${\log _5}25 = 2$as an exponential form?

Last updated date: 18th Jun 2024
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Hint: The given function is the logarithm function it can be defined as logarithmic functions are the inverses of exponential functions. By using one of the Basic Properties of logarithmic that is${\log _b}\left( x \right) = y$ we can write the given function as an exponential form.

The function from positive real numbers to real numbers to real numbers is defined as ${\log _b}:{R^ + } \to R \Rightarrow {\log _b}\left( x \right) = y$, if ${b^y} = x$, is called logarithmic function or the logarithm function is the inverse form of exponential function.
$y = {\log _b}\left( x \right)$, and the same equation written in exponential form,
${b^y} = x$. Let’s compare the two equations and look at what is the same and what is different. In both equations the y stays on the left side and the x stays on the right side, the only thing that moved was the b called the “base”. Identifying and moving the base is the key to changing from logarithmic form into exponential form.
$\Rightarrow {\log _5}25 = 2$
$i.e.,\,\,{\log _5}25 = 2$
$\therefore \,25 = {5^2}$
So, the correct answer is “$25 = {5^2}$”.
Note: The logarithmic equation can be converted to the exponential form. The exponential form of a number is defined as the number of times the number is multiplied by itself. The general form of logarithmic equation is ${\log _x}y = b$and it is converted to exponential form as $y = {x^b}$. Hence, we obtain the result or solution for the equation.