i have a problem here that has stumped me. any help is greatly appreciated, thanks in ADVANCE!
Use the rules $\displaystyle log_b(a) + log_b(c) = log_b(ac)$ and $\displaystyle klog_b(a) = log_b(a^k)$
$\displaystyle log_3(x^2(x-2)) = 2$
$\displaystyle x^2(x-2) = x^3-2x^2 = 3^2$
$\displaystyle x^3-2x^2-9 = 0$
and solve for x bearing in mind only solutions in which x > 2 counts for you can't have the log of a non-positive number
That does not, however, change the methods or processes. You still start by log rules to simplify the left-hand side, and then use the definition of logarithms to convert the equation to its equivalent exponential form. Then you solve the equation (which, for subtraction, is a rational equation).
If you get stuck, please reply showing how far you have gotten. Thank you!