How to solve #16 + 2^x = 2^(x+1)# without calculator?

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Answer 1 · 2018-05-09T00:02:16

#x=4#

Let's do our best to isolate #x# because that is what we are solving for. First subtract #2^x# from both sides of the equation.

#16=2^(x+1)-2^x#

Now use the properties of exponents to rewrite the right-hand side of the equation.

#16=2^x*2^1-2^x=2^x*2-2^x#

Now factor out #2^x# from the right-hand side of this equation.

#16=2^x(2-1)=2^x#

If you can't see that #x=4# from this equation rewrite #16# as #2^4#.

#2^4=2^x#

Now do you see that #x=4#?