If x is a positive real number such that:
4 log₁₀(x) + 4 log₁₀₀(x) + 8 log₁₀₀₀(x) = 13
Then, find the greatest integer not exceeding x.
Started 1 week ago by Admin in
Explanatory Answer
4 (log x / log 10) + 4 (log x / 2 log 10) + 8 (log x / 3 log 10) = 13
Simplifying:
4 log x + 2 log x + (8/3) log x = 13
(4 + 2 + 8/3) log x = 13
(26/3) log x = 13
log x = 13 * 3 / 26
log x = 3/2
x = 10^(3/2)
x = √1000 ≈ 31.62
The greatest integer not exceeding x = 31
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