1. ## Compass Placement Test

Hey guys,
I'm taking the math placement test and needed some help.
There was one problem that did not make any sense to me

(a^x2)(1/a^8x) Find X. Is this possible with two variables? I might have forgotten a part of the problem. Even if (a^x2)(1/a^8x)= 4 for example, i still wouldnt know how to solve it.

Thanks for all the help,

2. Originally Posted by usrnme14
Hey guys,
I'm taking the math placement test and needed some help.
There was one problem that did not make any sense to me

(a^x2)(1/a^8x) Find X. Is this possible with two variables? I might have forgotten a part of the problem. Even if (a^x2)(1/a^8x)= 4 for example, i still wouldnt know how to solve it.

Thanks for all the help,

you should post the full problem.

if for instance a > 0. then you can solve for x in terms of a by using the logarithm (to the base a), and then the quadratic formula.

$\displaystyle a^{x^2} \cdot \frac 1{a^{8x}} = 4$

$\displaystyle \Rightarrow a^{x^2 - 8x} = 4$ ..................since $\displaystyle \frac {x^a}{x^b} = x^{a - b}$

$\displaystyle \Rightarrow x^2 - 8x = \log_a 4$ ...............since $\displaystyle \log_a b = c \Longleftrightarrow a^c = b$

$\displaystyle \Rightarrow x^2 - 8x - \log_a 4 = 0$

now apply the quadratic formula ($\displaystyle \log_a 4 = 0$ is a constant)