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What will be the value of x if logx(1/5 1/12 1/21 1/21 1/32. infinity)2 = 2 AFTER LOG, x is the base and after the bracket 2 is square. Answer = 25/48. Please someone explain in detail?
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What will be the value of x if logx(1/5 1/12 1/21 1/21 1/32. infinity)...
**Solution:**
To solve the given equation, we need to understand the properties of logarithms and how they can be used to simplify the expression.
**Properties of logarithms:**
1. loga(xy) = loga(x) + loga(y)
2. loga(x/y) = loga(x) - loga(y)
3. loga(xn) = n * loga(x)
**Simplifying the expression:**
Let's simplify the given expression step by step:
logx(1/5) + logx(1/12) + logx(1/21) + logx(1/21) + logx(1/32) + logx(∞) = 2
Using property 1, we can combine the logarithms:
logx((1/5) * (1/12) * (1/21) * (1/21) * (1/32) * ∞) = 2
Simplifying the product inside the logarithm:
logx(1/(5 * 12 * 21 * 21 * 32 * ∞)) = 2
Since ∞ is not a specific number, we cannot directly calculate its value. However, we can simplify the expression further by recognizing that 1/∞ approaches 0 as ∞ gets larger.
logx(0) = 2
Since logx(0) is undefined, this equation has no solution. Therefore, there is no value of x that satisfies the equation logx(1/5 1/12 1/21 1/21 1/32 ∞)2 = 2.
The given answer of x = 25/48 is incorrect because the equation itself is invalid.
To solve the given equation, we need to understand the properties of logarithms and how they can be used to simplify the expression.
**Properties of logarithms:**
1. loga(xy) = loga(x) + loga(y)
2. loga(x/y) = loga(x) - loga(y)
3. loga(xn) = n * loga(x)
**Simplifying the expression:**
Let's simplify the given expression step by step:
logx(1/5) + logx(1/12) + logx(1/21) + logx(1/21) + logx(1/32) + logx(∞) = 2
Using property 1, we can combine the logarithms:
logx((1/5) * (1/12) * (1/21) * (1/21) * (1/32) * ∞) = 2
Simplifying the product inside the logarithm:
logx(1/(5 * 12 * 21 * 21 * 32 * ∞)) = 2
Since ∞ is not a specific number, we cannot directly calculate its value. However, we can simplify the expression further by recognizing that 1/∞ approaches 0 as ∞ gets larger.
logx(0) = 2
Since logx(0) is undefined, this equation has no solution. Therefore, there is no value of x that satisfies the equation logx(1/5 1/12 1/21 1/21 1/32 ∞)2 = 2.
The given answer of x = 25/48 is incorrect because the equation itself is invalid.
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What will be the value of x if logx(1/5 1/12 1/21 1/21 1/32. infinity)2 = 2 AFTER LOG, x is the base and after the bracket 2 is square. Answer = 25/48. Please someone explain in detail?
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What will be the value of x if logx(1/5 1/12 1/21 1/21 1/32. infinity)2 = 2 AFTER LOG, x is the base and after the bracket 2 is square. Answer = 25/48. Please someone explain in detail? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about What will be the value of x if logx(1/5 1/12 1/21 1/21 1/32. infinity)2 = 2 AFTER LOG, x is the base and after the bracket 2 is square. Answer = 25/48. Please someone explain in detail? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for What will be the value of x if logx(1/5 1/12 1/21 1/21 1/32. infinity)2 = 2 AFTER LOG, x is the base and after the bracket 2 is square. Answer = 25/48. Please someone explain in detail?.
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