Chapter 10: Q. 192 (page 1034)

In the following exercises,solve each logarithmic equation.
$\log_{a} 32 = 2$ .

Short Answer

Expert verified

$4 \sqrt{2}$

Step by step solution

Step 1.Given information

Consider the logarithmic equation $\log_{a} 32 = 2$ .

The logarithmic from $y = \log_{a} x$ is equivalent to exponential form $x = a^{y}$ .

Step 2.Solve the equation and find the value of a.

Comparing $\log_{a} 32 = 2$ with the standard form $y = \log_{a} x$ ,you have

$y = 2 a = a x = 32$

Convert logarithmic equation in exponential equation as shown below.

$x = a^{y} 32 = a^{2} a^{2} = 32$

So,the equation in the exponential form is $a^{2} = 32$

Now solve the equation using square root property

a = \pm \sqrt{32} = \pm 4 \sqrt{2} B e c a u s e t h e b a s e c a n' t b e n e g t i v e, s o e l i m i n a t e a = - 4 \sqrt{2} S o, t h e s o l u t i o n i s a = 4 \sqrt{2}

Step 3.Check

To check the solution,replace a by $4 \sqrt{2}$ in original equation.

$\log_{a} 32 = 2 \log_{4 \sqrt{2}} 32 = 2 [a = 4 \sqrt{2]} {(4 \sqrt{2})}^{2} = 32 32 = 32 [t r u e] T h e r e f o r e, t h e s o l u t i o n i s a = 4 \sqrt{2}$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercises,solve each logarithmic equation.
$\log_{a} 32 = 2$ .

Short Answer

Step by step solution

Step 1.Given information

Step 2.Solve the equation and find the value of a.

Step 3.Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Discrete Mathematics

Logic and Functions

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises,solve each logarithmic equation.loga32=2.

Short Answer

Step by step solution

Step 1.Given information

Step 2.Solve the equation and find the value of a.

Step 3.Check

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Applied Mathematics

Discrete Mathematics

Logic and Functions

Geometry

Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises,solve each logarithmic equation.
$\log_{a} 32 = 2$ .