# Question 645d2

Jul 6, 2017

I got: $x = 14.09017$

#### Explanation:

I would use a property of logs as:
logx+logy=log(xy)3 and write:

${\log}_{5} \left[\left(x - 11\right) \left(x - 6\right)\right] = 2$

then use the definition of log to write:

$\left(x - 11\right) \left(x - 6\right) = {5}^{2}$

$\left(x - 11\right) \left(x - 6\right) = 25$

rearrange:

${x}^{2} - 6 x - 11 x + 66 - 25 = 0$

${x}^{2} - 17 x + 41 = 0$

${x}_{1 , 2} = \frac{17 \pm \sqrt{289 - 164}}{2} =$
${x}_{1} = 14.09017$
${x}_{2} = 2.90903$
${x}_{2}$ is small and would make the arguments of the original logs negative.