how do you solve 4^x + 2^(x+2)-5=0? I know the answer is supposed to be 0 but I dont know how you get that. Can you please show all steps?

Question

anonymous · Answer

i think a good first step would be to write 
$$4^x+4\times 2^x-5=0$$ because $2^{x+2}=2^x\times 2^2=4\times 2^x$

anonymous · Answer

a good next step is 
$$4^x=2^{2x}$$ making your equation 
$$2^{2x}+4\times 2^x-5=0$$ so you have a quadratic equation in $2^x$ which you can probably solve by factoring

anonymous · Answer

$$(2^x-1)(2^x+5)=0$$
$$2^x=1$$ or$$2^x=-5$$ second one is impossible, first one is true only if $x=0$

anonymous · Answer

thank you. Can most problems like this be solved this way?