Module 1: Basic Concepts - Logarithms - Practice Problems


Instructions:: Work these problems on a sheet of paper and check your answers against those provided below.

#1

Express the following logarithmic functions as exponential functions.

Log₁₀ (150) = x
Log₁₀ (55) = x
Ln (500) = x
Ln (65) = x

Answer:

10^x = 150
10^x = 55
e^x = 500
e^x = 65

#2

Solve the following:

Log₁₀ (1,000) = x
Log₁₀ (59) = x
Log₁₀ (300) = x

Answer: i. x = 3

Solution:

Log₁₀ (1,000) = x can be rewritten as

10^X = 1000 where x = 3

Answer:

ii. x = 1.7709

iii. x = 2.4771

#3

Simplify the following:

Log₁₀ (ab) Log₁₀ (a)
Log₁₀ (ab) + Log₁₀ (b)
Log₁₀ (50) + Log₁₀ (265) Log₁₀ (315)

Answer: i. Log₁₀ (b)

Solution:

Answer: ii. Log₁₀ (a) +2 Log₁₀ (b)

Solution:

Answer: iii. 4

Solution:

Answer: iv. 1.6239

Solution:

#4

Solve the following:

4.8 e³ = x
24e⁴ + 2.7e^3.1 = x
9.6e^4.9 4.9e^1.2 = x

Answer: i. x = 96.41

Solution:

i. 4.8e³ = 4.8

20.086 = 96.41

Answer: ii. 1,370.29

Solution:

Answer: iii. 1,272.91

Solution:

#5

Solve the following:

Ln (1000) = x
Ln (e³) = x
Ln (128) + Ln (3.2) = x

Answer:

i. x = 6.91

ii. x = 3

Answer: iii. x = 6.015

Solution:

iii. 4.852 + 1.163 = 6.015

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Logarithms

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Module 1: Basic Concepts - Logarithms - Practice Problems

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