Which of the following values of t would satisfy the expression log10(25 – t) – log24 = log10t – 2 log105?
Which of the following values of t would satisfy the expression log10(25 – t) – log24 = log10t – 2 log105? Correct Answer 5
Given, log10(25 – t) – log24 = log10t – 2 log105 LHS ➩ log10(25 – t) – log24 ➩ log10(25 – t) – log222 ➩ log10(25 – t) – 2 ➩ log10(25 – t) – log10 100 ➩ log10((25 – t) / 100) RHS ➩ log10t – 2 log105 ➩ log10t – log1052 ➩ log10t – log1025 ➩ log10(t / 25) On equating RHS and LHS gives, ➩ t / 25 = 25 – t / 100 ➩ t = 25 – t / 4 ➩ 4t = 25 – t ➩ 5t = 25 ➩ t = 5
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Feb 20, 2025