Chapter 11: Q. 190 (page 1069)

In the following exercises,solve each logarithmic equation.
$\log_{a} 8 = 3$

Short Answer

Expert verified

a=2.

Step by step solution

Step 1.Given information

Consider the logarithmic equation $\log_{a} 8 = 3$ .

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 $\log_{a} 8 = 3$ with the standard form $y = \log_{a} x$ , you have $y = 3, a = a, x = 8$

Convert logarithmic equation in the exponential equation as shown below.

$x = a^{y} 8 = a^{3} a^{3} = 8$

So, the equation of the exponential form is $a^{3} = 8$

Now solve the equation as,

${(a^{3})}^{\frac{1}{3}} = {(8)}^{\frac{1}{3}} [R a i s e R a d i c a l] = {(2^{3})}^{\frac{1}{3}} {(a)}^{3 \frac{1}{3}} = {(2)}^{3 \frac{1}{3}} (a) = 2 S o, t h e s o l u t i o n i s a = 2$

To check the solution, replace a with 2 in the original equation

$\log_{a} 8 = 3 \log_{2} 8 = 3 [a = 2] 2^{3} = 8 8 = 8 [t r u e]$

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In the following exercises,solve each logarithmic equation.
$\log_{a} 8 = 3$

Short Answer

Step by step solution

Step 1.Given information

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

One App. One Place for Learning.

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In the following exercises,solve each logarithmic equation.loga8=3

Short Answer

Step by step solution

Step 1.Given information

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

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Decision Maths

Calculus

Logic and Functions

Pure Maths

Discrete Mathematics

Statistics

Study anywhere. Anytime. Across all devices.

In the following exercises,solve each logarithmic equation.
$\log_{a} 8 = 3$