Expert: Paul Klarreich - 5/7/2007

Question
Hi, I need some help solving 2^(x+1)(8^-x)=4.  Thankyou.

Answer
Questioner:   Ashley
Category:  Advanced Math

Question:  Hi, I need some help solving 2^(x+1)(8^-x)=4.  Thankyou
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Hi, Ashley,

This is an exponential equation.  You want everything to be written with a common base.  In this case, it is nice that  4 = 2^2  and that  8 = 2^3.  So you can use 2 as your common base.

2^(x+1)(8^-x) = 4

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

For (2^3)^-x remember the rule for a power of a power:  keep the base, multiply exponents.

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

Apply the rule for multiplying powers of a common base: keep the base, add exponents.

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

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

Now you have like bases, so the exponents must be equal:

1 - 2x = 2

- 2x = 1
x = - 1/2

Check:

2^(-1/2+1)(8^1/2) = 4

2^(1/2)(8^1/2) = 4

sqrt(2) sqrt(8) = 4

sqrt(16) = 4

4 = 4  CHECK!