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Setting $Y:=-(\ln X + 0.0064) = -\ln(e^{0.0064}X)$, we get an equation: $$Ye^Y = -\frac{0.08}{e^{0.0064}},$$ implying that $Y = W( -\frac{0.08}{e^{0.0064}} )$, where $W$ is Lambert W function. Then $$X = e^{- W( -\frac{0.08}{e^{0.0064}} ) - 0.0064}.$$

In Sage:

exp(-lambert_w(-0.08/exp(0.0064)) - 0.0064 )

gives 1.08359901378819. You can also try other branches of $W$, like:

exp(-lambert_w(-0.08/exp(0.0064),1) - 0.0064 )

which gives 0.563525163706476, etc.

Setting $Y:=-(\ln X + 0.0064) = -\ln(e^{0.0064}X)$, we get an equation: $$Ye^Y = -\frac{0.08}{e^{0.0064}},$$ implying that $Y = W( -\frac{0.08}{e^{0.0064}} )$, where $W$ is Lambert W function. function. Then $$X = e^{- W( -\frac{0.08}{e^{0.0064}} ) - 0.0064}.$$

In Sage:

exp(-lambert_w(-0.08/exp(0.0064)) - 0.0064 )

gives 1.08359901378819. You can also try other branches of $W$, like:

exp(-lambert_w(-0.08/exp(0.0064),1) - 0.0064 )

which gives 0.563525163706476, etc.

Setting $Y:=-(\ln X + 0.0064) = -\ln(e^{0.0064}X)$, we get an equation: $$Ye^Y = -\frac{0.08}{e^{0.0064}},$$ implying that $Y = W( -\frac{0.08}{e^{0.0064}} )$, where $W$ is Lambert W function. Then $$X = e^{- W( -\frac{0.08}{e^{0.0064}} ) - 0.0064}.$$

In Sage:

exp(-lambert_w(-0.08/exp(0.0064)) - 0.0064 )

gives 1.08359901378819. You can also try other branches of $W$, like:

exp(-lambert_w(-0.08/exp(0.0064),1) exp(-lambert_w(1, -0.08/exp(0.0064)) - 0.0064 )

which gives 0.56352516370647658.6383141226570 - 91.0209263484521*I, etc.

Setting $Y:=-(\ln X + 0.0064) = -\ln(e^{0.0064}X)$, we get an equation: $$Ye^Y = -\frac{0.08}{e^{0.0064}},$$ implying that $Y = W( -\frac{0.08}{e^{0.0064}} )$, where $W$ is Lambert W function. Then $$X = e^{- W( -\frac{0.08}{e^{0.0064}} ) - 0.0064}.$$

In Sage:

exp(-lambert_w(-0.08/exp(0.0064)) - 0.0064 )

gives 1.08359901378819. You can also try other branches of $W$, like:

exp(-lambert_w(1, exp(-lambert_w(-1, -0.08/exp(0.0064)) - 0.0064 )

which gives 58.6383141226570 - 91.0209263484521*I48.6340483659129, etc.

Setting $Y:=-(\ln X + 0.0064) = -\ln(e^{0.0064}X)$, we get an equation: $$Ye^Y = -\frac{0.08}{e^{0.0064}},$$ implying that $Y = W( -\frac{0.08}{e^{0.0064}} )$, where $W$ is Lambert W function. Then $$X = e^{- W( -\frac{0.08}{e^{0.0064}} ) - 0.0064}.$$

In Sage:Sage we can define a function that computes $X$ depending on a branch of $W$:

exp(-lambert_w(-0.08/exp(0.0064)) - 0.0064 )

gives 1.08359901378819. You can also try other branches of $W$, like:

exp(-lambert_w(-1, def X(branch=0):
    exp(-lambert_w(branch, -0.08/exp(0.0064)) - 0.0064 )

which Then X(0) gives 1.08359901378819, X(-1) gives 48.6340483659129, etc.and other branches give various complex solutions.

Setting $Y:=-(\ln X + 0.0064) = -\ln(e^{0.0064}X)$, we get an equation: $$Ye^Y = -\frac{0.08}{e^{0.0064}},$$ implying that $Y = W( -\frac{0.08}{e^{0.0064}} )$, where $W$ is Lambert W function. Then $$X = e^{- W( -\frac{0.08}{e^{0.0064}} ) - 0.0064}.$$

In Sage we can define a function that computes $X$ depending on a branch of $W$:

def X(branch=0):
    return exp(-lambert_w(branch, -0.08/exp(0.0064)) - 0.0064 )

Then X(0) gives 1.08359901378819, X(-1) gives 48.6340483659129, and other branches give various complex solutions.