Question

consider the logarithmic equation $log_{6}(1296) = 4$.
what is the base?
base
what is the exponent?
exponent
what is the argument?
argument
what is $log_{6}(1296) = 4$ in exponential form?

Explanation:

Step1: Identify log base

For $\log_b(x)=y$, base is $b$.
Here, $\log_6(1296)=4$, so base = 6.

Step2: Identify log exponent

For $\log_b(x)=y$, exponent is $y$.
Here, $\log_6(1296)=4$, so exponent = 4.

Step3: Identify log argument

For $\log_b(x)=y$, argument is $x$.
Here, $\log_6(1296)=4$, so argument = 1296.

Step4: Convert to exponential form

Use $\log_b(x)=y \iff b^y=x$.
Substitute values: $6^4=1296$.

Answer:

Base: 6
Exponent: 4
Argument: 1296
Exponential form: $6^4=1296$