/*! 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 96 Solve each equation. $$ 3|\l... [FREE SOLUTION] | 91影视

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Chapter 4: Problem 96

Solve each equation. $$ 3|\log x|-6=0 $$

Short Answer

Expert verified
The solutions for the equation are \( x = 10^2 \) and \( x = 10^{-2} \), which in numerical terms are \( x = 100 \) and \( x = 0.01 \).

Step by step solution

01

Solve for absolute value

To begin with, isolate the absolute value by adding 6 to both sides of the equation and then dividing by 3. This gives us the equation \( |\log x| = 2 \).
02

Break up the absolute value

Next, remember that the absolute value of a number is equal to the number itself if it is positive or zero, and its opposite if it is negative. Therefore, \( |\log x| = 2 \) means \( \log x = 2 \) or \( \log x = -2 \).
03

Convert to exponential form

Remember that the base of a common logarithm (when no base is written) is 10, so we can rewrite these equations in exponential form. Therefore \( x = 10^2 \) for the first equation and \( x = 10^{-2} \) for the second equation.

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Most popular questions from this chapter

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