Chapter 5: Q. 6 (page 351)

Solve each equation
$\log_{b} 16 = 2$

Short Answer

Expert verified

The value of b is 4

Step by step solution

Step 1. Given Information

Given equation $\log_{b} 16 = 2$

We have to solve equation for the value of b.

Step 2. Solution

Logarithmic function is good defined only if the argument of logarithmic function is a positive real number and base is a positive real number and not 1 $(\log_{b} x, x > 0, b > 0, b \neq 1)$ .

Therefore the solution of equation $\log_{b} 16 = 2$ must be $b > 0, b \neq 1 - - - (1)$

(Since b is at the base of the logarithmic function)

Using the formula:

$y \log_{a} x \Leftrightarrow x = a^{y} a > 0, a \neq 1 w h e r e a = b, x = 16 a n d y = 2 w e g e t : \log_{b} 16 = 2 b^{2} = 16 b = \pm 4$

The solution is greater that 0 and its not 1 (condition (1)), so the solution of the given equation is b = 4 .

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Solve each equation
$\log_{b} 16 = 2$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solution

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Solve each equationlogb16=2

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Solution

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Probability and Statistics

Theoretical and Mathematical Physics

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Study anywhere. Anytime. Across all devices.

Solve each equation
$\log_{b} 16 = 2$