To convert the given logarithmic equation into its exponential form, follow these steps:
### Step-by-Step Solution:
1. Understand the Definition of Logarithms:
The logarithmic equation [tex]\(\log_t(b) = z\)[/tex] means that [tex]\(z\)[/tex] is the power to which the base [tex]\(t\)[/tex] must be raised to yield the number [tex]\(b\)[/tex].
2. Convert to Exponential Form:
By the definition of logarithms, if [tex]\(\log_t(b) = z\)[/tex], then this can be rewritten in exponential form as:
[tex]\[
t^z = b
\][/tex]
### Explanation:
- The base [tex]\(t\)[/tex] of the logarithm becomes the base of the exponent.
- The logarithm result [tex]\(z\)[/tex] becomes the exponent.
- The argument [tex]\(b\)[/tex] becomes the result of the exponentiation.
### Result:
The given logarithmic equation [tex]\(\log_t(b) = z\)[/tex] in exponential form is:
[tex]\[
t^z = b
\][/tex]
