Compass Placement Test

Quote:

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,

Adam

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.

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

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

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

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

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