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Algebra II

3.13.3 Test (CST): Exponents, Logarithms, \& Their Graphs

Question 8 of 20

Which exponential equation is equivalent to the logarithmic equation below?

[tex]\[ 2=\ln x \][/tex]

A. [tex]\[ e = x^2 \][/tex]

B. [tex]\[ x = 2e \][/tex]

C. [tex]\[ x = e^2 \][/tex]

D. [tex]\[ x = 10^2 \][/tex]

Sagot :

GinnyAnsweridn
To convert the given logarithmic equation into its equivalent exponential form, follow these steps:

1. Understand the logarithmic equation provided:
[tex]\[ 2 = \ln(x) \][/tex]

2. Recall the definition of the natural logarithm:
The natural logarithm, [tex]\( \ln(x) \)[/tex], is the power to which the base [tex]\( e \)[/tex] (Euler's number, approximately 2.71828) must be raised to produce the number [tex]\( x \)[/tex]. Specifically, if [tex]\( \ln(x) = 2 \)[/tex], then:
[tex]\[ e^2 = x \][/tex]

3. By converting from logarithmic form to exponential form, we have:
[tex]\[ x = e^2 \][/tex]

Therefore, the exponential equation that is equivalent to the logarithmic equation [tex]\( 2 = \ln(x) \)[/tex] is:
[tex]\[ x = e^2 \][/tex]

Thus, the correct choice is:
C. [tex]\( x = e^2 \)[/tex]
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