Chapter 8: Q. 13 (page 556)

Solve $\log_{3} (x + 8) + \log_{3} (x) = 2$ .

Short Answer

Expert verified

The value ofxis 1.

Step by step solution

Step 1. given Information

The given equation is $\log_{3} (x + 8) + \log_{3} (x) = 2$ .

Step 2. Use Logarithmic Properties

Use the property $\log_{a} x + \log_{a} y = \log_{a} (x y)$ and simplify the equation.

$\log_{3} ((x + 8) x) = 2$

Now, use the property, $\log_{a} x = y \Leftrightarrow x = a^{y}$ to rewrite the equation.

$x (x + 8) = 3^{2} x (x + 8) = 9$

Step 3. Solve the Quadratic Equation

The obtained equation can be simplified to $x^{2} + 8 x - 9 = 0$ .
Factor the equation and find its roots.

$\begin{array}{rcl} x^{2} + 9 x - x - 9 & = & 0 \\ (x + 9) (x - 1) & = & 0 \\ x & = & 1, - 9 \end{array}$

The logarithmic functions are not defined on negative integers.
So, $x = 1$ .

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Solve $\log_{3} (x + 8) + \log_{3} (x) = 2$ .

Short Answer

Step by step solution

Step 1. given Information

Step 2. Use Logarithmic Properties

Step 3. Solve the Quadratic Equation

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Solve log3x+8+log3x=2.

Short Answer

Step by step solution

Step 1. given Information

Step 2. Use Logarithmic Properties

Step 3. Solve the Quadratic Equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Probability and Statistics

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Discrete Mathematics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

Solve $\log_{3} (x + 8) + \log_{3} (x) = 2$ .