SOLUTION: Can you help me with this please? -evaluate without calculator the square root of 2 ^x+4 = 4^x

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Question 924212: Can you help me with this please?
-evaluate without calculator
the square root of 2 ^x+4 = 4^x

Found 2 solutions by ewatrrr, Edwin McCravy:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
2 ^x+4 = 4^x
2 ^x+4 = (2^2)^x
2 ^x+4 = 2^(2x)
x+ 4 = 2x
4 = x

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
2^x+4 = 4^x
If you meant

2^(x+4) = 4^x

which means 

2%5E%28x%2B4%29+=+4%5Ex

2%5E%28x%2B4%29+=+%282%5E2%29%5Ex

2%5E%28x%2B4%29+=+2%5E%282x%29

Since the bases are positive, equal, and not 1,
the exponts are alse equal:

x%2B4=2x

4=x

-----------------------------

That's probably what you meant.  But when you don't enclose
the exponent inside of parentheses like this

2^(x+4) = 4^x

then what you wrote

2^x+4 = 4^x
means this:

2%5Ex%2B4+=+4%5Ex

2%5Ex%2B4+=+%282%5E2%29%5Ex

2%5Ex%2B4+=+2%5E%282x%29

2%5Ex%2B4+=+2%5E%28x%2A2%29

2%5Ex%2B4+=+%282%5Ex%29%5E2

%282%5Ex%29%5E2-2%5Ex-4=0

Then we'd have to use the quadratic formula and 
solve by taking logs and the answer is this complicated
expression:

x+=+%28ln%281%2Bsqrt%2817%29%29-ln%282%29%29%2F%28ln%282%29%29

When typing mathematical expressions and equations, you must
enclose numerators, denominators and exponents in parentheses
except when they contain only one number or only one letter

Edwin