If 3(X +1) = 5(X - 2), then find the value of x. (Take log 5 = 0.6989 and log…
2025
If 3(X +1) = 5(X - 2), then find the value of x.
(Take log 5 = 0.6989 and log 3 = 0.4771)
- A.
5
- B.
7.5
- C.
11
- D.
8.5
Attempted by 6 students.
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Correct answer: D
Solution: Solve 3^(x+1) = 5^(x-2) by taking logarithms and using the given values log 5 = 0.6989 and log 3 = 0.4771.
Take logs: (x + 1) log 3 = (x - 2) log 5.
Rearrange to collect x terms: x·log 3 - x·log 5 = -2·log 5 - log 3, so x (log 3 - log 5) = - (2 log 5 + log 3).
Solve for x: x = (2 log 5 + log 3)/(log 5 - log 3).
Substitute the given values: numerator = 2×0.6989 + 0.4771 = 1.8749; denominator = 0.6989 − 0.4771 = 0.2218.
Compute x = 1.8749 / 0.2218 ≈ 8.453, which rounds to 8.5. Thus the correct value is 8.5.