How do you solve log_6 u–log_6 9=2?

Feb 4, 2015

The result should be $u = 324$

You start using a property of logarithms where you have:
${\log}_{a} \left(x\right) - {\log}_{a} \left(y\right) = {\log}_{a} \left(\frac{x}{y}\right)$

and the basic definition of logarithm: ${\log}_{a} \left(x\right) = b$ $\to$ $x = {a}^{b}$

And using these in your example:

${\log}_{6} \left(\frac{u}{9}\right) = 2$ and so:
$\frac{u}{9} = {6}^{2}$
$u = 9 \cdot {6}^{2}$
$u = 324$