To convert the logarithmic equation [tex]\( \log_{10}(10000) = 4 \)[/tex] into its exponential form, follow these steps:
1. Identify the base of the logarithm. In this case, the base is 10.
2. Recognize that the logarithmic equation [tex]\( \log_{10}(10000) = 4 \)[/tex] implies that the base raised to the power of the result equals the argument of the logarithm.
3. Write the equivalent exponential form. Using our example, this means raising 10 to the power of 4 to get 10000.
So we rewrite [tex]\( \log_{10}(10000) = 4 \)[/tex] in exponential form as:
[tex]\[ 10^4 = 10000 \][/tex]
Therefore, the exponential form of the equation is:
[tex]\[ 10^4 = 10000 \][/tex]
This shows that raising the base 10 to the power of 4 results in 10000.
