If #2^x + 2^x + 2^x + 2^x = 2^7#, what is the value of #x#?

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Answer 1 · 2016-02-08T04:27:49

#x=5#

Note that there are #4# of the #2^x# terms. These can be grouped as if they were any other term, giving us the simplified expression:

#4(2^x)=2^7#

There are a couple courses of action we could take here. I will divide both sides by #4#.

#2^x=2^7/4#

To do this without working out #2^7#, we can recall that #2^2=4#.

#2^x=2^7/2^2#

To divide exponential terms with the same base, use the rule:

#x^a/x^b=x^(a-b)#

Here, this gives us

#2^x=2^(7-2)=2^5#

Now, since we have the same base, it follows logically that we can equate the powers.

#x=5#