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Precalculus Enhanced with Graphing Utilities

Sullivan

$Math Studyset 91影视 Explanations$ Math

6th Edition 路 1200 pages

ISBN: 9780321795465

Chapter 5: Q 20. (page 297)

Change the given logarithmic statement to an equivalent statement involving an exponent.
$\log_{b} (4) = 2$

Short Answer

Expert verified

The equivalent exponential statement of the given logarithmic statement is $b^{2} = 4$ .

Step by step solution

01

Step 1. Given information

A logarithmic statement is given as $\log_{b} (4) = 2$ .

02

Step 2. Formula Used

The logarithmic function $y = \log_{a} (x)$ can be changed into an exponential statement as $x = a^{y}$ .

03

Step 3. Conversion

The logarithmic statement is $\log_{b} (4) = 2$ .

Compare statement with y=log(x).

$x = 4, a = b$ , and $y = 2$

So, the corresponding exponential statement is

$b^{2} = 4$

01

Step 1. Given information

A logarithmic statement is given as $\log_{b} (4) = 2$ .

02

Step 2. Formula Used

The logarithmic function $y = \log_{a} (x)$ can be changed into an exponential statement as $x = a^{y}$ .

03

Step 3. Conversion

The logarithmic statement is $\log_{b} (4) = 2$ .

Compare statement with $y = \log_{a} (x)$ .

role="math" localid="1647952214454" $x = 4, a = b$ , and $y = 2$

So, the corresponding exponential statement is

$b^{2} = 4$

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Most popular questions from this chapter

Solve the equation $2^{- x} = 16$

and verify your results using a graphing utility

The graphs of $y = a^{- x}$ and $y = {[\frac{1}{a}]}^{x}$ are identical. Why?

solve each equation. Verify your results using a graphing utility.

$9^{- x + 15} = 27^{x}$

solve each equation. Verify your results using a graphing utility.

$3^{x^{2} - 7} = 27^{2 x}$

The domain of one to one function g is $[0, 15]$ ,and its range is $(0, 8)$ . State the domain and range of $g^{- 1}$

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