Determine whether the following statements are true and give a...

Question

Determine whether the following statements are true and give an explanation or counterexample.

$2 = \ln 2^{e}$

Accepted Answer

Welcome back. Everyone determine the validity of the given statement. 15 equals Ln of 15 to the power of E A says true and B says false. So what we're going to do is simply use one of the properties of logarithms. We can essentially rewrite a number in terms of a natural logarithm. Let's remember that if we take the natural logarithm of E, that's simply one. But if E is raised to the power of B, then we get B itself since we can bring that exponent down and the land of E is simply one, right? So we can use this property to rewrite 15. Now our B is 15. So we're going to get a land of E to the power of 15th, that would be equal to 15. So now we're going to essentially check if Alan of E to the power of 15 is equal to a land of 15 to the power of E. And since we're comparing logs, well, we are essentially going to say that E to the power of 15 must be equal to 15 to the power of E. And these are not equal numbers. So we can essentially state that the given statement is false and the correct answer to this problem is Option B, thank you for watching.

Determine whether the following statements are true and give an explanation or counterexample.

$2 = \ln 2^{e}$

Key Concepts

Natural Logarithm

Exponential Functions

Equality of Functions

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