Chapter 10: Q. 201 (page 1034)

In the following exercises, solve each logarithmic equation.
$\log_{4} (3 x - 2) = 2$

Short Answer

Expert verified

The solution is $x = 6$ .

Step by step solution

Step 1. Rewrite in exponential form and simplify.

Consider the logarithmic equation $\log_{4} (3 x - 2) = 2$ .

Its equivalent exponential form is given as

$4^{2} = 3 x - 2$

On simplifying we get,

$16 = 3 x - 2$

Step 2. Solve for x

Add $2$ to both sides of the equation.

$\begin{array}{rcl} 16 + 2 & = & 3 x - 2 + 2 \\ 18 & = & 3 x \end{array}$

Now divide both sides by $3$ .

$\begin{array}{rcl} \frac{18}{3} & = & \frac{3 x}{3} \\ 6 & = & x \end{array}$

Step 3. Check the solution

Substitute $6$ for $x$ in the original equation, we get

$\begin{array}{rcl} \log_{4} (3 \times 6 - 2) & = & 2 \\ \log_{4} (18 - 2) & = & 2 \\ \log_{4} (16) & = & 2 \\ 4^{2} & = & 16 \\ 16 & = & 16 \end{array}$

So we get a true statement, thus the found solution is correct.

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In the following exercises, solve each logarithmic equation.
$\log_{4} (3 x - 2) = 2$

Short Answer

Step by step solution

Step 1. Rewrite in exponential form and simplify.

Step 2. Solve for x

Step 3. Check the solution

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In the following exercises, solve each logarithmic equation. log43x-2=2

Short Answer

Step by step solution

Step 1. Rewrite in exponential form and simplify.

Step 2. Solve for x

Step 3. Check the solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Decision Maths

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Statistics

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Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, solve each logarithmic equation.
$\log_{4} (3 x - 2) = 2$