2x = ln(4e^x -1)?
回答 (1)
2015-12-30 12:16 pm
2x = ln(4 e^x -1)
e^(2x) = e^[ln (4 e^x - 1)]
e^(2x) = 4 e^x - 1 = 0
e^(2x) - 4 e^x + 1 = 0
e^x = [4 + √(4² - 4)] / 2 或 [4 - √(4² - 4)] / 2
e^x = 2 + √3 或 2 - √3
ln e^x = ln (2 + √3) 或 ln (2 - √3)
x = ln (2 + √3) 或 ln (2 - √3)
x ≈ 1.316957897 或 -1.316957897
e^(2x) = e^[ln (4 e^x - 1)]
e^(2x) = 4 e^x - 1 = 0
e^(2x) - 4 e^x + 1 = 0
e^x = [4 + √(4² - 4)] / 2 或 [4 - √(4² - 4)] / 2
e^x = 2 + √3 或 2 - √3
ln e^x = ln (2 + √3) 或 ln (2 - √3)
x = ln (2 + √3) 或 ln (2 - √3)
x ≈ 1.316957897 或 -1.316957897
收錄日期: 2021-04-20 16:09:19
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