It is easy that $x = 2$ below, but can I solve it with a general formula?
$$4^x + 2^x = 20$$
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1Try the substitution $y = 2^{x}$. – user0102 Feb 09 '21 at 20:18
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2Hint: $4^x = (2^x)^2$ – player3236 Feb 09 '21 at 20:18
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For this particular question, you can note that if $x < y$, then $2^x + 4^x < 2^y + 4^y$ and hence, the equation can have at most one root. You have already found one by inspection. – Aryaman Maithani Feb 09 '21 at 20:28
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but if the equation is more difficult to solve by inspections. Lets say, 0.94^x + 0.5^x = 1. Now I cant factorize any term to make same base. (if that was the hint :)) – Roktiv Feb 09 '21 at 20:50
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Do the substitution $t=2^x$, then solve the quadratic equation you get. Undo the subsitution, you will have to decide whether one answer works or not.
Gowexx
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