Write the logarithmic equation in exponential form. For example, the exponential form of ln(5) = 1.6094... is e1.6094... = 5.lne3 = 3e3 =

Conversion of Logarithmic Equation to Exponential Form

To convert a logarithmic equation to its exponential form, we use the definition of logarithms. A general logarithmic equation of the form:

$\log_b(a) = c$

can be expressed in exponential form as:

$b^c = a$

Example

Given the logarithmic equation $\ln(5) = 1.6094...$:

1. Identify the base: In natural logarithms, the base $b$ is $e$.
2. Identify $a$ and $c$: Here, $a = 5$ and $c = 1.6094...$.

Exponential Form

Thus, the exponential form of the equation is:

$e^{1.6094...} = 5$

Final Answer

The exponential form of $\ln(5) = 1.6094...$ is $e^{1.6094...} = 5$.