SOLUTION: solve for x in 4^5x×2^(3x)2=256

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Question 1022021: solve for x in 4^5x×2^(3x)2=256

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!
4^5x×2^(3x)2=256
It's impossible to tell from that what's part of exponent 
and what is not. When typing everything all on one line, 
you must use parentheses to enclose each part, remembering 
that the rule is PEMDAS so it won't be ambiguous.  It could 
be interpreted as any of these or some others, all which 
have different solutions:

4%5E5x%2A2%5E%283x%292%22%22=%22%22256 or 4%5E%285x%29%2A2%5E%283x%29%2A2%22%22=%22%22256 or 4%5E%285x%29%2A%282%5E%283x%29%292%22%22=%22%22256

I will arbitrarily assume it's

4%5E%285x%29%2A%282%5E%283x%29%29%5E2%22%22=%22%22256

Write 4 as 22 and 256 as 28

%282%5E2%29%5E%285x%29%2A%282%5E%283x%29%29%5E2%22%22=%22%222%5E8

When the base of an exponential is itself an exponential,
we simplify by multiplying exponents across the parentheses:

2%5E%2810x%29%2A2%5E%286x%29%22%22=%22%222%5E8

Now we add the exponents of 2 on the left in order to
multiply exponentials with the same base 2:

2%5E%2816x%29%22%22=%22%222%5E8

Since we have a single power of 2 on both sides, we
can drop the base 2 and equate the exponent:

16x%22%22=%22%228

x%22%22=%22%228%2F16

x%22%22=%22%221%2F2

Edwin