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Chapter 3: Problem 61

Write the exponential equation in logarithmic form. $$e^{1 / 2}=1.6487 \ldots$$

Short Answer

Expert verified
The logarithmic form of the given equation \(e^{1 / 2}=1.6487 \ldots\) is \(log_e(1.6487 \ldots)=1 / 2\).

Step by step solution

01

Understand the relation

Before starting the conversion, understand that exponential and logarithm forms are two ways of expressing the same thing. The exponential form is base^exponent=result, while the logarithm form is log_base(result)=exponent.
02

Identify base, exponent, and result from exponential form

From the given equation \(e^{1 / 2}=1.6487 \ldots\), \(e\) is the base, \(1 / 2\) is the exponent, and \(1.6487 \ldots\) is the result (to some number of decimal places).
03

Replace in the logarithmic format

Put these values into the logarithmic form. Which gives us, log_e(1.6487 \ldots) = 1 / 2

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Most popular questions from this chapter

Solve the equation algebraically. Round the result to three decimal places. Verify your answer using a graphing utility. $$\frac{1-\ln x}{x^{2}}=0$$

Solve the logarithmic equation algebraically. Approximate the result to three decimal places. $$4 \log (x-6)=11$$

$$\$ 2500$$ is invested in an account at interest rate \(r\), compounded continuously. Find the time required for the amount to (a) double and (b) triple. $$r=0.0375$$

The demand equation for a hand-held electronic organizer is \(p=5000\left(1-\frac{4}{4+e^{-0.002 x}}\right)\) Find the demand \(x\) for a price of (a) \(p=\$ 600\) and (b) \(p=\$ 400\).

The amount of time (in hours per week) a student utilizes a math-tutoring center roughly follows the normal distribution \(y=0.7979 e^{-(x-5.4)^{2} / 0.5},\) \(4 \leq x \leq 7,\) where \(x\) is the number of hours. (a) Use a graphing utility to graph the function. (b) From the graph in part (a), estimate the average number of hours per week a student uses the tutoring center.
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