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I have the equation x = a*b^x and want to solve it for x. But every online solver I tried says that it is not possible.

But when I choose a==8 and b==0.5 there is a solution for x==2

Is it not possible to solve the equation formally?

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closed as off topic by Igor Rivin, Steven Landsburg, Emil Jeřábek, Bill Johnson, Todd Trimble Dec 6 '12 at 15:43

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The eager closers have done their (dirty) work here. If you want more information about this use of the Lambert W function, try asking at one of the other locations found in the FAQ. For example math.stackexchange.com –  Gerald Edgar Dec 6 '12 at 16:05
    
Thanks for your comment! –  Rick Dec 6 '12 at 21:14

1 Answer 1

up vote 2 down vote accepted

There are no elementary formulas for such equations. Using the Lambert W function, the solution is $$x = -\frac{W(-a \log b)}{\log b}$$

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