Converting Logarithmic to Exponential Equation

Logarithms are the opposite of exponents. Thus, a logarithmic equation can be converted to an equivalent exponential equation.

`log_2(8) = 3` is the same equation as `2^3 = 8`.

Any logarithmic equation has three parts:

1. Base of logarithm (the number written in subscript after logarithm; 2 in the above example)
2. Argument of logarithm (the number written after the base in line with 'log'; 8 in the above example)
3. Result (the number after the = sign; 8 in the above equation)

Similarly, any exponential equation has three parts:

1. Base of exponent (2 in the above example)
2. Exponent (or power, or index; 3 in the above example)
3. Result (8 in the above example)

To convert a logarithmic equation to an exponential equation, we use the following concepts:

1. Base of logarithm becomes base of exponent
2. Argument of logarithm becomes result of exponential equation
3. Result of logarithmic equation becomes exponent

Consider the logarithmic equation `log_{10}(100) = 2`,

1. Base is 10
2. Argument is 100
3. Result is 2

According to the concepts explained above, we will change the above numbers as follows:

1. Base of logarithm, 10, becomes base in the exponential equation
2. Argument 100 becomes result of exponential equation
3. Result of logarithmic equation, 2, becomes exponent

Thus, the equivalent exponential equation to `log_{10}(100) = 2` is `10^2 = 100`.