Q.76 solve each equation. Express irr... [FREE SOLUTION]

91影视

Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q.76 (page 316)

solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places:
$\log_{2} (3 x + 2) - \log_{4} (x) = 3$

Short Answer

Expert verified

The value of x satisfying the equation is $x = 0.078 a n d x = 5.69$

Step by step solution

Given information

We are given a equation $\log_{2} (3 x + 2) - \log_{4} (x) = 3$

Change the base

We have,

$\log_{2} (3 x + 2) - \log_{4} (x) = 3 \log_{2} (3 x + 2) - \frac{\log_{2} (x)}{\log_{2} {(2)}^{2}} = 3 \log_{2} (3 x + 2) - \frac{\log_{2} (x)}{2} = 3 2 \log_{2} (3 x + 2) - \log_{2} (x) = 6$

Solve the equation

We get,

$2 \log_{2} (3 x + 2) - \log_{2} (x) = 6 l {og}_{2} {(3 x + 2)}^{2} - \log_{2} (x) = 6 \log_{2} \frac{{(3 x + 2)}^{2}}{x} = 6$

Now use the formula $y = \log_{a} (x) 鈬� x = a^{y}$

$\frac{{(3 x + 2)}^{2}}{x} = 2^{6} {(3 x + 2)}^{2} = 64 x 9 x^{2} + 12 x + 4 = 64 x 9 x^{2} - 52 x + 4 = 0$

Find the value of x

We get,

$9 x^{2} - 52 x + 4 = 0 x = \frac{52 卤 \sqrt{52^{2} - 4 (9) (4)}}{18} x = \frac{52 卤 \sqrt{2704 - 144}}{18} x = \frac{52 卤 50.59}{18} x = \frac{52 + 50.59}{18} o r x = \frac{52 - 50.59}{18} x = 5.69 o r x = 0.078$

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91影视

solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places:
$\log_{2} (3 x + 2) - \log_{4} (x) = 3$

Short Answer

Step by step solution

Given information

Change the base

Solve the equation

Find the value of x

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

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91影视

solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places: log2(3x+2)-log4(x)=3

Short Answer

Step by step solution

Given information

Change the base

Solve the equation

Find the value of x

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Pure Maths

Discrete Mathematics

Calculus

Geometry

Logic and Functions

Study anywhere. Anytime. Across all devices.

solve each equation. Express irrational solutions in exact form and as a decimal rounded to three decimal places:
$\log_{2} (3 x + 2) - \log_{4} (x) = 3$