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Chapter 4: Problem 93

Evaluate or simplify each expression without using a calculator. $$e^{\ln 125}$$

Short Answer

Expert verified
The simplified expression is 125

Step by step solution

01

Recognize the property of natural logarithm

We firstly need to recognize that the exercise involves a property of the exponential function and the natural logarithm. In this case, the property is \(e^{\ln a} = a\), for any positive number \(a\). This comes from the fact that the natural logarithm, \(\ln(x)\), is the inverse function of the exponential function with base \(e\), \(e^x\).
02

Apply the property

Now we can apply this property to the expression \(e^{\ln 125}\). Using this property, we can simplify the given expression by setting \(a = 125\) as following: \(e^{\ln 125} = 125\).

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Most popular questions from this chapter

Explain how to use the graph of \(f(x)=2^{x}\) to obtain the graph of \(g(x)=\log _{2} x\).

Logarithmic models are well suited to phenomena in which growth is initially rapid but then begins to level off. Describe something that is changing over time that can be modeled using a logarithmic function.

Evaluate the indicated logarithmic expressions without using a calculator. a. Evaluate: \(\log _{2} 32\) b. Evaluate: \(\log _{2} 8+\log _{2} 4\) c. What can you conclude about \(\log _{2} 32,\) or \(\log _{2}(8 \cdot 4) ?\)

Find the domain of each logarithmic function. $$f(x)=\ln \left(x^{2}-4 x-12\right)$$

Evaluate the indicated logarithmic expressions without using a calculator. a. Evaluate: \(\log _{3} 81\) b. Evaluate: \(2 \log _{3} 9\) c. What can you conclude about $$\log _{3} 81, \text { or } \log _{3} 9^{2} ?$$
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