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64e^x+3=1/32
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Solve 64e^x + 3 = 1/32.
Subtract 3: 64 e^x = 1/32 - 3 = -95/32.
Then e^x = (-95/32)/64 = -95/2048, which is negative. Since e^x > 0 for all real x, there is no real solution.
If complex solutions are allowed, write
x = ln(−95/2048) = ln(95/2048) + i(π + 2πk), k ∈ Z,
or equivalently
x = ln 95 − 11 ln 2 + i(2k+1)π, k ∈ Z.
Subtract 3: 64 e^x = 1/32 - 3 = -95/32.
Then e^x = (-95/32)/64 = -95/2048, which is negative. Since e^x > 0 for all real x, there is no real solution.
If complex solutions are allowed, write
x = ln(−95/2048) = ln(95/2048) + i(π + 2πk), k ∈ Z,
or equivalently
x = ln 95 − 11 ln 2 + i(2k+1)π, k ∈ Z.
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