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If x is a positive quantity such that 2x = 3log52.then x is equal to
- a)log5 8
- b)1 + log3(5 / 3)
- c)log5 9
- d)1 + log5(3 / 5)
Correct answer is option 'D'. Can you explain this answer?
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If x is a positive quantity such that 2x = 3log52.then x is equal toa...
Given that: 2x = 3log5 2
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=> 2x = 2log53
=>x = log53
=> x = log5 (3 * 5 / 5)
=> x = log5 5 + log5 (3 / 5)
=> x = 1 + log5 5
Hence, option D is the correct answer.
Most Upvoted Answer
If x is a positive quantity such that 2x = 3log52.then x is equal toa...
To solve the given equation, let's start by simplifying the right-hand side of the equation:
2x = 3log52
Now, we can rewrite the equation using the property of logarithms that states: logb(x^y) = ylogb(x)
2x = log52^3
Simplifying further:
2x = log525
Now, we can rewrite the equation in exponential form:
5^2x = 25
Taking the logarithm of both sides, we get:
log5(5^2x) = log525
Using the property of logarithms again:
2xlog5(5) = log525
Since log5(5) = 1, we have:
2x = log525
Now, we can simplify the right-hand side of the equation:
2x = 2
Dividing both sides by 2:
x = 1
Therefore, the value of x is 1.
Now let's compare the value of x with the answer options given:
a) log5 8: This is not equal to 1, so it is not the correct answer.
b) 1 log3(5 / 3): This is not equal to 1, so it is not the correct answer.
c) log5 9: This is not equal to 1, so it is not the correct answer.
d) 1 log5(3 / 5): This is equal to 1, so it is the correct answer.
Therefore, the correct answer is option 'D', 1 log5(3 / 5).
2x = 3log52
Now, we can rewrite the equation using the property of logarithms that states: logb(x^y) = ylogb(x)
2x = log52^3
Simplifying further:
2x = log525
Now, we can rewrite the equation in exponential form:
5^2x = 25
Taking the logarithm of both sides, we get:
log5(5^2x) = log525
Using the property of logarithms again:
2xlog5(5) = log525
Since log5(5) = 1, we have:
2x = log525
Now, we can simplify the right-hand side of the equation:
2x = 2
Dividing both sides by 2:
x = 1
Therefore, the value of x is 1.
Now let's compare the value of x with the answer options given:
a) log5 8: This is not equal to 1, so it is not the correct answer.
b) 1 log3(5 / 3): This is not equal to 1, so it is not the correct answer.
c) log5 9: This is not equal to 1, so it is not the correct answer.
d) 1 log5(3 / 5): This is equal to 1, so it is the correct answer.
Therefore, the correct answer is option 'D', 1 log5(3 / 5).
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