1. ## exponential functions..

just a quick question, what am I doing wrong here? x = 5/2

(1/4)^(1-x) = 8

4^(-1+1-x) = 2^3

4^(-x) = 2^3

2^2(-x) = 2^3

2(-x) = 3

-x = 3/2

x = -3/2 ?

2. $\displaystyle (1/4)^{1 - x} = 8$

$\displaystyle (2^{-2})^{1 - x} = 2^3$

$\displaystyle 2^{-2 + 2x} = 2^3$

$\displaystyle -2 + 2x = 3$

$\displaystyle 2x = 5$

$\displaystyle x =\frac{5}{2}$

3. Originally Posted by 1+1bob
just a quick question, what am I doing wrong here? x = 5/2

4^(-1+1-x) = 2^3
Here

4. Originally Posted by 1+1bob
just a quick question, what am I doing wrong here? x = 5/2

(1/4)^(1-x) = 8

4^(-1+1-x) = 2^3

4^(-x) = 2^3

2^2(-x) = 2^3

2(-x) = 3

-x = 3/2

x = -3/2 ?
the line highlighted red is where you made the mistake. you should not have added the powers, you should have multiplied them. we add powers when we multiply two numbers having the same base. here we were raising a number to a power. we multiply the powers in this case