[Math] Solving Exponential Equations with Addition of Bases

exponential function

I was given this equation,

$$4^x + 4^{x+1} = 40$$

I know that $x = 1.5$, but the problem lies with the solution. I have tried searching for examples with the same situation but there seems to be less detail on how they come up with the answer.

Best Answer

Hint:

I suppose that your equation is $$ 4^x +4^{x+1}=40 $$ that is $$ 4^x+4\cdot4^x=40 \iff 4^x(1+4)=40 \iff 5\cdot 4^x=40 $$

can you do from this?

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