Solving Exponential Equations with Addition of Bases

Question

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.

Answer 1

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?

Answer 2

$${ 4 }^{ x }+4{ \times 4 }^{ x }=40\\ { 4 }^{ x }\times \left( 1+4 \right) =40\\ { 4 }^{ x }=8\\ { 2 }^{ 2x }={ 2 }^{ 3 }\\ 2x=3\\ x=1.5$$