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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. 216 (page 1035)

Explain why $\log_{a} a^{x} = x$ .

Short Answer

Expert verified

Logarithm function and exponential functions are inverses of each other so $\log_{a} a^{x} = x$

Step by step solution

01

Step 1. statement

The exponential function is the inverse of the logarithm function

so $x = \log_{a} y y = a^{x}$ are equivalent.

02

Step 2. verification

Substitute $a^{x}$ for $y$ in the equation $x = \log_{a} y$

$x = \log_{a} y x = \log_{a} a^{x}$

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Most popular questions from this chapter

In the following exercises, solve each equation.

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

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

$f (x) = - 5 x - 4$

In the following exercises, graph each exponential function:

$f (x) = 3^{x + 2}$

On the same coordinate system, graph:

$f (x) = 4^{x}$

$g (x) = 4^{x} - 2$

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

$f (x) = 4^{x}, g (x) = 4^{x} + 2$

See all solutions

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