UPSC Exam > UPSC Questions > logx(4) = 1/3, then x =?a)4b)32c)64d)16Correc...
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logx(4) = 1/3, then x =?
- a)4
- b)32
- c)64
- d)16
Correct answer is 'C'. Can you explain this answer?
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logx(4) = 1/3, then x =?a)4b)32c)64d)16Correct answer is 'C'. Can you ...
Rewrite logx(4)=1/3 in exponential form using the definition of a logarithm. If x and b are positive real numbers and b≠1, then log b(x)=y is equivalent to b^y = x.x^1/3 = 4Raise each side of the equation to the 3/1 power to eliminate the fractional exponent on the left side.(x^1/3)^3/1 = (4)^3/1Simplify the right side.x = 64Verify each of the solutions by substituting them back into the original equation logx(4) = 1/3and solving. In this case, all solutions were found to be valid.x=64
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logx(4) = 1/3, then x =?a)4b)32c)64d)16Correct answer is 'C'. Can you ...
Solution:
Given, logx(4) = 1/3.
To find x, we can use the definition of logarithms.
The logarithm of a number to a particular base is the power to which the base must be raised to get the number.
That is, logx(4) = 1/3 can be written as x^(1/3) = 4.
Now, let's solve for x.
x^(1/3) = 4
Cubing both sides, we get
x^(1/3) * x^(1/3) * x^(1/3) = 4 * 4 * 4
x^(1) = 64
Therefore, x = 64.
Hence, the correct option is (C).
Given, logx(4) = 1/3.
To find x, we can use the definition of logarithms.
The logarithm of a number to a particular base is the power to which the base must be raised to get the number.
That is, logx(4) = 1/3 can be written as x^(1/3) = 4.
Now, let's solve for x.
x^(1/3) = 4
Cubing both sides, we get
x^(1/3) * x^(1/3) * x^(1/3) = 4 * 4 * 4
x^(1) = 64
Therefore, x = 64.
Hence, the correct option is (C).
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logx(4) = 1/3, then x =?a)4b)32c)64d)16Correct answer is 'C'. Can you ...
Here... -->> 4=x^1/3 =>x=64...
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logx(4) = 1/3, then x =?a)4b)32c)64d)16Correct answer is 'C'. Can you explain this answer?
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