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Chapter 5: Q. 135 (page 301)

In the definition of the logarithmic function, the basea is not allowed to be equal 1. Why?

Short Answer

Expert verified

x=1 is not an exponential function but it is a constant function.

Step by step solution

01

Step 1. Introduction

By the definition of a logarithmic function, we can write y=logxas an exponential function we need to write why the logarithmic function the baseais not allowed to equal1.

02

Step 2. Explanation

If logax=y鈬�x=ay

then, log1x=y鈬�x=1y=1

That is, x=1ory=1is not an exponential function but it is a constant function.

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Most popular questions from this chapter

If g(-5)=3 and g is one-to-one, what is g-1(3)?

Begin with the graph of y=exand use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

fx=e-x

The function f(x)=|x|is not one-to-one. Find a suitable restriction on the domain of f so that the new function that results is one-to-one. Then find the inverse of f.

Solve the equation3x3=9x

and verify your results using a graphing utility.

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

5x2+8=1252x
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