Thread: Need help with exponential equations

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 8² instead of just 8?

2^x = 2³

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.

We are given:



Using the property of exponents we may rewrite the equation as:









Divide through by 7:



Hence:

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

Originally Posted by dirtyharry

...

I don't understand this part:



Wouldn't



be 2^x + 4^x + 8^x = 56?

How did you come up with the "1"?

Note that:



is not the same as:



To make things simpler to see, let then we have:



Now combine like terms on the left:



Divide both sides by 7:



Back-substitute for :



You see, when I factored in my first post, I used the fact that each term on the left has as a factor.

Originally Posted by MarkFL2

Note that:



is not the same as:



To make things simpler to see, let then we have:



Now combine like terms on the left:



Divide both sides by 7:



Back-substitute for :



You see, when I factored in my first post, I used the fact that each term on the left has as a factor.

Thanks