Solve for x of an exponential function

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SUMMARY

The discussion focuses on solving the exponential equation e^(2x+9) - 4e^x - 5 = 0. The user initially transformed the equation to e^(2x+9) = 4e^x + 5 and attempted to apply logarithms. However, the solution was effectively reached by substituting u = e^x, converting the equation into a quadratic form, which can be solved easily. The final step involves reverting back to x using x = ln(u).

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Homework Statement



e^(2x+9) - 4e^x -5 = 0

Homework Equations





The Attempt at a Solution


I changed this into: e^(2x+9) =4e^x + 5
I took logarithm of both sides:
2x+9=ln(4e^x +5)

but i don't know what to do with the right hand side.
what will be the easiest way to solve this?
Thank you very much
 
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Try this,
[tex]\begin{align*}<br /> 0 & = e^{ 2 x + 9 } - 4 e^x - 5 \\<br /> & = e^9 e^{ 2 x } - 4 e^x - 5.<br /> \end{align*}[/tex]

Then the substitution [tex]u=e^x[/tex] turns this into a quadratic equation, which is easily solved, and then [tex]x = \ln u[/tex].
 
excellent.
thank you v much
 

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