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The question is "The solution of $2^{2x+3} = 2^{x+1} + 3$ can be expressed in the form $a + \log_2 (b)$ where $a,b$ are integers. Find the value of $a$ and $b$."

I tried putting $\log_2$ on both sides but I couldn't do anything after that because the argument on the right hand side is a sum. Any help is appreciated.

Bernard
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Fern Adams
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  • In general, it is a good idea to look for patterns, sometimes this will lead somewhere useful. For example, factor the $2^{x+1}$ out as @user715522 has done. – copper.hat Jan 22 '20 at 19:14

1 Answers1

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Hint:

$$2\cdot2^{2\left(x+1\right)}-2^{\left(x+1\right)}-3=0$$

now use $2^{\left(x+1\right)}=t$