/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 10 Find a number \(x\) such that \(... [FREE SOLUTION] | 91影视

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Chapter 3: Problem 10

Find a number \(x\) such that \(\ln x=-3\).

Short Answer

Expert verified
The value of \(x\) that satisfies the equation \(\ln x = -3\) is approximately \(0.0498\).

Step by step solution

01

Rewrite the natural logarithm equation as an exponential equation

Recall that the natural logarithm function is the inverse function of the exponential function, \(e^x\). Therefore, we can rewrite the equation \(\ln x = -3\) as an exponential equation: \[e^{-3} = x\]
02

Evaluate the exponential function

Now that we have an exponential equation, we can evaluate the exponential function: \[x = e^{-3}\]
03

Calculate the value of x

Using a calculator to find the value of \(e^{-3}\), we get: \[x \approx 0.0498\] So, the value of \(x\) that satisfies the equation \(\ln x = -3\) is approximately \(0.0498\).

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Most popular questions from this chapter

Find all numbers \(x\) that satisfy the given equation. \(\frac{\ln (12 x)}{\ln (5 x)}=2\)

Find all numbers \(x\) that satisfy the given equation. \(\ln (x+5)+\ln (x-1)=2\)

Estimate the indicated value without using a calculator. \(\ln 1.003\)

Show that the range of \(\sinh\) is the set of real numbers.

Find a number \(y\) such that \(\ln y=4\).
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