Loading [MathJax]/jax/output/HTML-CSS/jax.js
Skip to main content
Library homepage
 

Text Color

Text Size

 

Margin Size

 

Font Type

Enable Dyslexic Font
Mathematics LibreTexts

1.5.1: Exercises 1.5

( \newcommand{\kernel}{\mathrm{null}\,}\)

Terms and Concepts

Exercise 1.5.1.1

Explain the relationship between logarithmic functions and exponential functions.

Answer

For the same base, they are inverses of each other.

Exercise 1.5.1.2

What questions are you answering when you evaluate log5(25)?

Answer

25 is 5 raised to what power?

Exercise 1.5.1.3

What is the value of the base for ln(x)?

Answer

e

Exercise 1.5.1.4

Explain why logarithms help solve exponential statements.

Answer

Logarithms help solve exponential statements because logarithms and exponentials are inverse functions.

Problems

Evaluate the given statement in exercises 1.5.1.51.5.1.8.

Exercise 1.5.1.5

log3(81)

Answer

4

Exercise 1.5.1.6

ln(e5.7)

Answer

5.7

Exercise 1.5.1.7

eln(x)

Answer

1x

Exercise 1.5.1.8

4log2(22)

Answer

16

Write the given statement as a single simplified logarithm in exercises 1.5.1.91.5.1.12.

Exercise 1.5.1.9

4log3(2x)log3(y2)

Answer

log3(16x4y2)

Exercise 1.5.1.10

23ln(x)+3ln(2y)

Answer

ln(8x2/3y3)

Exercise 1.5.1.11

(2x)log2(3)+log2(5)

Answer

log2(5(32x))

Exercise 1.5.1.12

3ln(xy)2ln(x2y)

Answer

ln(yx)

In exercises 1.5.1.131.5.1.17, solve the given problem for x, if possible. If a problem cannot be solved, explain why.

Exercise 1.5.1.13

5x=25

Answer

x=2

Exercise 1.5.1.14

5x=5

Answer

Not possible; we cannot raise a positive number to a power and get a negative number.

Exercise 1.5.1.15

5x=0

Answer

Not possible; we cannot raise a positive number to a power and get a zero.

Exercise 1.5.1.16

5x=0.2

Answer

x=1

Exercise 1.5.1.17

5x=1

Answer

x=0

In exercises 1.5.1.181.5.1.25, solve the given problem for x.

Exercise 1.5.1.18

3x6=2

Answer

x=6+log3(2)

Exercise 1.5.1.19

42x5=3

Answer

x=5+log4(3)2

Exercise 1.5.1.20

25x+6=4

Answer

x=45

Exercise 1.5.1.21

6x+π=2

Answer

x=log6(2)π

Exercise 1.5.1.22

(16)3x2=36x+1

Answer

x=0

Exercise 1.5.1.23

15=8ln(3x)+7

Answer

x=13e11/4

Exercise 1.5.1.24

2x=3x1

Answer

x=ln(3)ln(2)ln(3)

Exercise 1.5.1.25

8=4ln(2x+5)

Answer

x=e252


This page titled 1.5.1: Exercises 1.5 is shared under a CC BY-NC license and was authored, remixed, and/or curated by Amy Givler Chapman, Meagan Herald, Jessica Libertini.

Support Center

How can we help?