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If log 5=0.6990, then find log 125 and 500?
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If log 5=0.6990, then find log 125 and 500?
Given:
log 5 = 0.6990
To find:
log 125 and log 500
Solution:
We know that log a^b = b * log a. Using this property, we can find the values of log 125 and log 500.
Finding log 125:
125 = 5^3
Using the property mentioned above, we can write:
log 125 = 3 * log 5
Substituting the given value of log 5 = 0.6990, we have:
log 125 = 3 * 0.6990
log 125 = 2.0970
Therefore, log 125 = 2.0970.
Finding log 500:
500 = 5^3 * 2^2
Using the property mentioned above, we can write:
log 500 = 3 * log 5 + 2 * log 2
Substituting the given value of log 5 = 0.6990, and log 2 = 0.3010 (log 2 is a commonly known value), we have:
log 500 = 3 * 0.6990 + 2 * 0.3010
log 500 = 2.0970 + 0.6020
log 500 = 2.6990
Therefore, log 500 = 2.6990.
Summary:
- log 125 = 2.0970
- log 500 = 2.6990
log 5 = 0.6990
To find:
log 125 and log 500
Solution:
We know that log a^b = b * log a. Using this property, we can find the values of log 125 and log 500.
Finding log 125:
125 = 5^3
Using the property mentioned above, we can write:
log 125 = 3 * log 5
Substituting the given value of log 5 = 0.6990, we have:
log 125 = 3 * 0.6990
log 125 = 2.0970
Therefore, log 125 = 2.0970.
Finding log 500:
500 = 5^3 * 2^2
Using the property mentioned above, we can write:
log 500 = 3 * log 5 + 2 * log 2
Substituting the given value of log 5 = 0.6990, and log 2 = 0.3010 (log 2 is a commonly known value), we have:
log 500 = 3 * 0.6990 + 2 * 0.3010
log 500 = 2.0970 + 0.6020
log 500 = 2.6990
Therefore, log 500 = 2.6990.
Summary:
- log 125 = 2.0970
- log 500 = 2.6990
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If log 5=0.6990, then find log 125 and 500?
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If log 5=0.6990, then find log 125 and 500? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If log 5=0.6990, then find log 125 and 500? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If log 5=0.6990, then find log 125 and 500?.
If log 5=0.6990, then find log 125 and 500? for CAT 2025 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about If log 5=0.6990, then find log 125 and 500? covers all topics & solutions for CAT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for If log 5=0.6990, then find log 125 and 500?.
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