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# if 4^(x+5)=2^(3x+1) then what is x

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if 4^(x+5)=2^(3x+1) then what is x

Guest Jun 30, 2014

#1
+576
+8

The reason this looks so challenging is because we are dealing with two different bases, 4 and 2.  The good news is that it is relatively simple to convert our base 4 to base 2 because 2^2=4

It looks like this

(2^2)^(x+5)=2^(3x+1)

we have a common base now but need to simplify the left side of the equation

2^(2(x+5))=2^(3x+1)

2^(2x+10)=2^(3x+1)

now that we have a common base on both sides of the equation it must be the case that our exponents are equivalent.

2x+10=3x+1

10=x+1

9=x

jboy314  Jun 30, 2014
Sort:

#1
+576
+8

The reason this looks so challenging is because we are dealing with two different bases, 4 and 2.  The good news is that it is relatively simple to convert our base 4 to base 2 because 2^2=4

It looks like this

(2^2)^(x+5)=2^(3x+1)

we have a common base now but need to simplify the left side of the equation

2^(2(x+5))=2^(3x+1)

2^(2x+10)=2^(3x+1)

now that we have a common base on both sides of the equation it must be the case that our exponents are equivalent.

2x+10=3x+1

10=x+1

9=x

jboy314  Jun 30, 2014

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