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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 10: Q. 184 (page 1034)

In the following exercises, solve each logarithmic equation.
$y = \log_{\frac{1}{3}} (x)$

Short Answer

Expert verified

The graph is

Step by step solution

01

Given information

Given the function $y = \log_{\frac{1}{3}} (x)$

02

Rewriting in exponential form

Rewriting, we get

$y = \log_{\frac{1}{3}} (x) {(\frac{1}{3})}^{y} = x$

03

Use the point plotting method

Using point plotting, we get

$y$	${(\frac{1}{3})}^{y} = x$	$(x, y)$
$0$	$1$	$(1, 0)$
$- 1$	$3$	$(3, - 1)$
$1$	$\frac{1}{3}$	$(\frac{1}{3}, 1)$

04

Sketching the graph by plotting points

Plotting the points, we get

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Most popular questions from this chapter

In the following exercises, find the inverse of each function.

$f (x) = 8 x$

On the same coordinate system, graph:

$f (x) = 3^{x}$

$g (x) = 3^{x + 1}$

In the following exercises, solve each equation.

$3^{x^{2} - 2 x} = \frac{1}{3}$

In the following exercises, graph each function in the same coordinate system:

$f (x) = 2^{x}, g (x) = 2^{x + 2}$

In the following exercises, graph each function in the same coordinate system:

$f (x) = 2^{x}, g (x) = 2^{x} - 1$

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