We are given:
Using the property of exponents we may rewrite the equation as:
Divide through by 7:
Hence:
2^{x }+ 2^{x+1} + 2^{x+2} = 56
The solution is the following:
2^{x} + 2 * 2^{x}+ 4 * 2^{x} = 56
Why is that? I don't understand how it came to this. Where did the 4 come from? How come there's so many 2s?
7 * 2^{x} = 56
2^{x} = 8
How did 56 turn into 8? Shouldn't it be 8^{2} instead of just 8?
2^{x} = 2^{3 }x = 3
I only understand the last two steps. Please help, I need to know this (and more) for a test. This isn't the only equation that confuses me, but it would help to know what lead to the final solution.
Please reply,
thanks.
Thanks, now I know how the conversion to multiplying occured.
However, I don't understand this part:
Wouldn't
be 2^{x }+ 4^{x} + 8^{x }= 56?
How did you come up with the "1"?
Also, about dividing through by 7: 7 is not their common denominator - 2 is not in seven (at least not without a decimal). How does it stay unchanged? Is it because of the X?
Thanks