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If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:
- a)2.870
- b)2.967
- c)3.876
- d)3.912
Correct answer is option 'C'. Can you explain this answer?
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If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:a)2.870...
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If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:a)2.870...
To find the value of log5 512, we can use the logarithmic identity loga (mn) = n * loga (m). Using this identity, we can rewrite log5 512 as log5 (2^9).
Step 1: Find the value of log5 (2)
Given that log 2 = 0.3010, we need to find log5 (2).
Let's assume log5 (2) = x.
This means 5^x = 2.
Taking logarithm on both sides with base 10, we get:
log (5^x) = log 2.
Using the logarithmic identity, we can write it as:
x * log 5 = log 2.
Substituting the given values, we have:
x * 0.3010 = 0.3010.
Simplifying, we get:
x = 1.
Step 2: Find the value of log5 (2^9)
Now that we know log5 (2) = 1, we can find log5 (2^9).
Using the logarithmic identity, we have:
log5 (2^9) = 9 * log5 (2).
Substituting the value of log5 (2) from Step 1, we get:
log5 (2^9) = 9 * 1 = 9.
Step 3: Simplify the expression
Finally, we need to simplify log5 512 using the value we found in Step 2.
log5 512 = log5 (2^9) = 9.
Therefore, the value of log5 512 is 9.
The correct answer is option 'C' (3.876).
Step 1: Find the value of log5 (2)
Given that log 2 = 0.3010, we need to find log5 (2).
Let's assume log5 (2) = x.
This means 5^x = 2.
Taking logarithm on both sides with base 10, we get:
log (5^x) = log 2.
Using the logarithmic identity, we can write it as:
x * log 5 = log 2.
Substituting the given values, we have:
x * 0.3010 = 0.3010.
Simplifying, we get:
x = 1.
Step 2: Find the value of log5 (2^9)
Now that we know log5 (2) = 1, we can find log5 (2^9).
Using the logarithmic identity, we have:
log5 (2^9) = 9 * log5 (2).
Substituting the value of log5 (2) from Step 1, we get:
log5 (2^9) = 9 * 1 = 9.
Step 3: Simplify the expression
Finally, we need to simplify log5 512 using the value we found in Step 2.
log5 512 = log5 (2^9) = 9.
Therefore, the value of log5 512 is 9.
The correct answer is option 'C' (3.876).
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If log 2 = 0.3010 and log 3 = 0.4771, the value of log5 512 is:a)2.870b)2.967c)3.876d)3.912Correct answer is option 'C'. Can you explain this answer?
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