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Chapter 3: Problem 54

Writing a Natural Logarithmic Equation In Exercises \(53-56,\) write the exponential equation in logarithmic form. $$e^{1 / 2}=1.6487 \ldots$$

Short Answer

Expert verified
The logarithmic form of the given exponential equation is \(\ln 1.6487 = 1/2\).

Step by step solution

01

Understand the Exponential Equation

Given is an exponential equation of the form \(e^{1 / 2}=1.6487 \ldots \). A base 'e' is raised to the power \(1/2\), and it equals approximately 1.6487.
02

Conversion to Logarithmic Form

A logarithmic form of the given exponential equation is obtained by switching the positions of the base and result, and placing the power as the result of the logarithm. Mathematically, the exponential equation \(e^{1 / 2}=1.6487 \ldots \) can be rewritten as \(\ln 1.6487 = 1/2\). Here, 'ln' represents the natural logarithm, which is the logarithm to the base 'e'.

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Most popular questions from this chapter

Use a graphing utility to graph and solve the equation. Approximate the result to three decimal places. Verify your result algebraically. $$5^{x}=212$$

Find the domain, \(x\) -intercept, and vertical asymptote of the logarithmic function and sketch its graph. $$g(x)=\ln (-x)$$

Use a graphing utility to graph and solve the equation. Approximate the result to three decimal places. Verify your result algebraically. $$8 e^{-2 x / 3}=11$$

Find the domain, \(x\) -intercept, and vertical asymptote of the logarithmic function and sketch its graph. $$h(x)=\ln (x+5)$$

Function \(\quad\) Value $$f(x)=3 \ln x \quad x=0.74$$
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