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# Rewrite the following equations in the logarithm from: ${{5}^{0}}=1$

Last updated date: 14th Jul 2024
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Hint: The exponential if of the form ${{b}^{y}}=x$. Convert it to logarithmic form $y={{\log }_{b}}x$, where b is the base of the number and b should be greater than zero (b> 0).

Logarithms were created to be the inverse of exponential function. To give us the ability to solve the problem $x={{b}^{y}}$ for y.
For $x>0$ and $b>0,b\ne 1,y={{\log }_{b}}x$ is equivalent to ${{b}^{y}}=x$.
From the definition of a logarithm we get two equations $y={{\log }_{b}}x$and ${{b}^{y}}=x$. The equations $y={{\log }_{b}}x$and ${{b}^{y}}=x$ are different ways of expressing the same thing. The equation $y={{\log }_{b}}x$ is written in logarithmic form and the equation ${{b}^{y}}=x$is written in exponential form. The two equations are just different ways of writing the same thing.
Here given ${{5}^{0}}=1$ of form ${{b}^{y}}=x$ [exponential]
\begin{align} & y={{\log }_{b}}x\Rightarrow 0={{\log }_{5}}x \\ & 0={{\log }_{5}}1 \\ & \Rightarrow {{\log }_{5}}1=0 \\ \end{align}