Sure, let's convert the given logarithmic equation into its exponential form step-by-step.
We are given the logarithmic equation:
[tex]\[
\log (b) = a
\][/tex]
Here, the logarithm is assumed to be with base 10, as no base is specified (this is the common convention unless otherwise stated). The general rule for converting a logarithmic equation to an exponential form is:
[tex]\[
\log_b(x) = y \implies b^y = x
\][/tex]
Now, applying this rule to our equation [tex]\(\log(b) = a\)[/tex]:
1. Identify the base of the logarithm. Since the base is not specified, it is assumed to be 10.
2. Rewrite the equation in exponential form, where the base is 10, the exponent is [tex]\(a\)[/tex], and the result is [tex]\(b\)[/tex].
So,
[tex]\[
\log_{10}(b) = a \implies 10^a = b
\][/tex]
Thus, the exponential form of [tex]\(\log(b) = a\)[/tex] is:
[tex]\[
10^a = b
\][/tex]
So, in summary, the exponential form of the logarithmic equation [tex]\(\log(b) = a\)[/tex] is:
[tex]\[
10^a = b
\][/tex]
