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Rewrite the equation in exponential form.

[tex] \ln(b) = n [/tex]

Include a multiplication sign between symbols. For example, [tex] a \cdot x [/tex].

[tex] e^n = b [/tex]

Examples:
- [tex] a \cdot x [/tex]
- [tex] \sin(a) [/tex]
- [tex] \frac{\partial}{\partial x} f [/tex]
- [tex] \infty [/tex]
- [tex] \Omega [/tex]

Sagot :

GinnyAnswer
To convert the logarithmic equation
[tex]\[ \ln(b) = n \][/tex]
into its exponential form, we need to make use of the fundamental relationship between logarithms and exponents. The natural logarithm (denoted as [tex]\(\ln\)[/tex]) is the inverse operation of exponentiation with the base [tex]\(e\)[/tex], where [tex]\(e\)[/tex] is Euler's number, approximately equal to 2.71828.

Here are the steps to rewrite the given logarithmic equation into exponential form:

1. Identify the logarithmic equation
[tex]\[ \ln(b) = n \][/tex]

2. Recall the property of logarithms: The natural logarithm [tex]\(\ln(b)\)[/tex] is equivalent to the power to which [tex]\(e\)[/tex] must be raised to obtain [tex]\(b\)[/tex]. This can be expressed as:
[tex]\[ \ln(b) = n \implies b = e^n \][/tex]

3. Rewrite the equation in exponential form: Using the above property, the equation [tex]\(\ln(b) = n\)[/tex] can be rewritten by exponentiating both sides to get [tex]\(b\)[/tex]. This gives us:
[tex]\[ b = e^n \][/tex]

Therefore, the exponential form of the logarithmic equation [tex]\(\ln(b) = n\)[/tex] is:

[tex]\[ b = e * n \][/tex]
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