Chapter 5: Q. 19 (page 315)

Solve the logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility.
$\log (2 x + 1) = 1 + \log (x - 2)$

Short Answer

Expert verified

The solution of the given logarithmic function is $\{\frac{21}{8}\} .$

Step by step solution

Step 1. Given information

$Thegivenequationis \log (2 x + 1) = 1 + \log (x - 2)$

We have to express irrational solutions in exact form and as a decimal rounded to three decimal places.

Also, we have to verify the result using the graphing utility.

Step 2. Simplify

$\begin{array}{l} Now, \\ \Rightarrow \log (2 x + 1) = 1 + \log (x - 2) \\ \Rightarrow \log (2 x + 1) = \log 10^{1} + \log (x - 2) [∵ a = \log_{b} b^{a}] \\ \Rightarrow \log (2 x + 1) = \log (10 \cdot (x - 2)) [∵ \log a + \log b = \log (a \cdot b)] \\ \Rightarrow 2 x + 1 = 10 (x - 2) \\ \Rightarrow 2 x + 1 = 10 x - 20 \\ \Rightarrow 2 x - 10 x = - 20 - 1 \\ \Rightarrow - 8 x = - 21 \\ \Rightarrow x = \frac{21}{8} \end{array}$

Step 3. Verifying the result

Plot the graph of the equation using the graphing utility as shown below.

From the above graph. we can observe that the graph of the given equation intersects the x-axis at $x = \{\frac{21}{8}\} .$

Therefore, the solution is verified.

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Solve the logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility.
$\log (2 x + 1) = 1 + \log (x - 2)$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify

Step 3. Verifying the result

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Solve the logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility.log2x+1=1+logx−2

Short Answer

Step by step solution

Step 1. Given information

Step 2. Simplify

Step 3. Verifying the result

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Mechanics Maths

Applied Mathematics

Pure Maths

Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

Solve the logarithmic equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places. Verify your results using a graphing utility.
$\log (2 x + 1) = 1 + \log (x - 2)$