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mathematics UK Year 13 Mathematics (A Levels)
 
Solved problems for the chapter:
 

Laws of logarithms

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Detailed solution steps are available at:
 
https://en.openprof.com/wb/chapter:laws_of_logarithms/5471/


Example 1.

Evaluate:


    
Example 2.

Calculate the following expression to two decimal places using a calculator:


    
3.

Express the following into its constituent logarithms where a, b and c are positive numbers:


    
4.

Simplify:




where a and b are positive numbers.

    
5.

Express each of the following into their constituent logarithms where a, b and c are positive numbers:





    
6.

Express the following into its constituent logarithms where a, b and c are positive numbers:


    
7.

Express the following into its constituent logarithms where a, b and c are positive numbers:


    
8.

Express the following into its constituent logarithms where a, b and c are positive numbers:


    

9.

Express the following into its constituent logarithms where a, b and c are positive numbers:


    
10.

Express the following into its constituent logarithms where a, b and c are positive numbers:


    
11.

Express the following into its constituent logarithms where a, b and c are positive numbers:


    
12.

Express the following into its constituent logarithms where a, b and c are positive numbers:


    
13.

Express the following into its constituent logarithms where a, b and c are positive numbers:


    
14.

Express the following into its constituent logarithms where a, b and c are positive numbers:


    
15.

Express the following into its constituent logarithms where a, b and c are positive numbers:


    
16.

Express as a sum or difference of simple logarithms:


    
17.

Express as a sum or difference of simple logarithms:


    
18.

Express as a sum or difference of simple logarithms:


    

19.

Express as a sum or difference of simple logarithms:


    
20.

Simplify:


    
21.

Simplify:


    
22.

Simplify:


    
23.

Simplify:


    
24.

Simplify the expression:


    
25.

Simplify the expression:


    
26.

Evaluate:


    
27.

Evaluate the expression:


    
28.

Evaluate the expression:


    

29.

Evaluate the expression:


    
30.

Evaluate the expression:


    
31.

Write the first term in base 2 and calculate the value of the expression:


    
32.

Evaluate:


    
33.

Calculate:


    
34.

Evaluate:


    
35.

Express as logarithm with base and calculate the value of the expression:


    
36.

Calculate the logarithm with a pocket calculator to 3 significant figures:


    
37.

Evaluate:


    
38.

Evaluate:


    

39.

Express as logarithm with base and calculate the value of the expression:


    
40.

Using a calculator, calculate to three significant figures:


    
41.

Evaluate the logarithm using the calculator leaving your result in three significant figures:


    
42.

Calculate the value of the expression:




where a, b, c and d are positive real numbers greater than 1.

    
43.

If find the value of the expression:


    
44.

Calculate without using a calculator:


    
45.

Calculate without using a calculator:


    
46.

Calculate without using a calculator: