SOLUTION: Good day Here's my question I'm struggling a bit with Solve for x: 2(to the power of x+2) + 2(to the power of x)/4 + 2(To the power of x) = 42 (2x+2 + 2X/4 + 2X = 42)

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Good day Here's my question I'm struggling a bit with Solve for x: 2(to the power of x+2) + 2(to the power of x)/4 + 2(To the power of x) = 42 (2x+2 + 2X/4 + 2X = 42)      Log On


   

Question 915390: Good day
Here's my question I'm struggling a bit with
Solve for x:
2(to the power of x+2) + 2(to the power of x)/4 + 2(To the power of x) = 42
(2x+2 + 2X/4 + 2X = 42)
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
2(to the power of x+2) + 2(to the power of x)/4 + 2(To the power of x) = 42

2^(x+2)+2^(x)/4+2^x=42

highlight_green%282%5E%28x%2B2%29%2B2%5E%28x%29%2F4%2B2%5Ex=42%29

%282%5Ex%29%282%5E2%29%2B%281%2F4%292%5Ex%2B2%5Ex=42

4%2A2%5Ex%2B%281%2F4%292%5Ex%2B2%5Ex=42

%284%2B1%2F4%2B1%292%5Ex=42

%285%261%2F4%292%5Ex=42

%2821%2F4%29%2A2%5Ex=42

2%5Ex=42%284%2F21%29

2%5Ex=%282%2A3%2A7%2A4%29%2F%283%2A7%29, this step helps with simplification.

2%5Ex=8

highlight%282%5Ex=2%5E3%29
x=3