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If log10a = b, find the value of 103b in terms of a.
- a)a3
- b)3a
- c)a x 1000
- d)a x 100
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
If log10a = b, find the value of 103bin terms of a.a)a3b)3ac)a x 1000d...
log10a = b ⇒ 10b = a ⇒ By definition of logs.
Thus 103b = (10b)3 = a3.
Most Upvoted Answer
If log10a = b, find the value of 103bin terms of a.a)a3b)3ac)a x 1000d...
Solution:
Given, log10a = b
We need to find the value of 103b in terms of a.
Let's solve this step by step.
Step 1: Find the value of 10b using the given equation.
log10a = b
10b = a
Step 2: Rewrite 103b as (10^3)b
103b = (10^3)b
Step 3: Substitute the value of 10b in the above equation.
103b = (10^3)b = (10^3)log10a
Step 4: Use the property of logarithms, loga^b = b*loga
(10^3)log10a = log10a^1000
Step 5: Substitute the value of log10a from the given equation.
log10a^1000 = loga^1000
Step 6: Simplify the expression.
loga^1000 = 3loga(a^3) = 3loga(a x a x a) = 3loga(a^3)
Step 7: Substitute the value of 3loga(a^3) in the expression obtained in Step 5.
103b = log10a^1000 = 3loga(a^3) = 3log10a = a3
Hence, the value of 103b in terms of a is a3.
Answer: (a) a3
Given, log10a = b
We need to find the value of 103b in terms of a.
Let's solve this step by step.
Step 1: Find the value of 10b using the given equation.
log10a = b
10b = a
Step 2: Rewrite 103b as (10^3)b
103b = (10^3)b
Step 3: Substitute the value of 10b in the above equation.
103b = (10^3)b = (10^3)log10a
Step 4: Use the property of logarithms, loga^b = b*loga
(10^3)log10a = log10a^1000
Step 5: Substitute the value of log10a from the given equation.
log10a^1000 = loga^1000
Step 6: Simplify the expression.
loga^1000 = 3loga(a^3) = 3loga(a x a x a) = 3loga(a^3)
Step 7: Substitute the value of 3loga(a^3) in the expression obtained in Step 5.
103b = log10a^1000 = 3loga(a^3) = 3log10a = a3
Hence, the value of 103b in terms of a is a3.
Answer: (a) a3
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Question Description
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