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Online Quiz (Worksheet A B C D)

Questions Per Quiz = 2 4 6 8 10

High School Mathematics
3.5 Problems on Logarithms - IX

Example:
Find the value of log3/4 (243/1024).
Solution:
Let log3/4 (243/1024) = x
Bye definition of logarithm
(3/4)x = 243/1024
Factors of 243 = 3*81
= 3 * 3 * 27
= 3 * 3 * 3 * 9
= 3 * 3 * 3 * 3 * 3
243 = 35
Factors of 1024 = 2 * 512
= 2 * 2 * 256
= 2 * 2 * 2 * 128
= 2 * 2 * 2 * 2 * 64
= 2 * 2 * 2 * 2 * 2 * 32
= 2 * 2 * 2 * 2 * 2 * 2 * 16
= 2 * 2 * 2 * 2 * 2 * 2 * 2 * 8
= 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 4
= 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2 * 2
1024 = 210 = (22)5 = 45
243/1024 = 35 / 45
= (3/4)5
(3/4)x =(3/4)5
Bases are equal so indices are equal.
Therefore, x = 5
i.e., log3/4 (243/1024) = 5
Directions: Solve the following problems. Also write at least ten examples of your own.
Q 1: Find the value of log7/9 (343/729).
3
5
4
2

Q 2: Find the value of log7/8 (49/64).
4
5
2
3

Q 3: Find the value of log5/7 (625/2401).
5
4
3
2

Q 4: Find the value of log11/3 (13331/27).
3
4
2
5

Q 5: Find the value of log3/4 (27/64).
3
2
5
4

Q 6: Find the value of log5/3 (3125/243).
2
4
3
5

Question 7: This question is available to subscribers only!

Question 8: This question is available to subscribers only!


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