Problem: The values of aaa in the equation: 10(a2−15a)=2\log _{10}\left(a^{2}-15 a\right)=2log10(a2−15a)=2 is:
Answer Choices:
A. 15±2332\dfrac{15 \pm \sqrt{233}}{2}215±233
B. 20,−520,-520,−5
C. 15±3052\dfrac{15 \pm \sqrt{305}}{2}215±305
D. ±20\pm 20±20
E. none of these Solution:
Since 10(a2−15a)=2\log _{10}\left(a^{2}-15 a\right)=2log10(a2−15a)=2, then a2−15a=102=100a^{2}-15 a=10^{2}=100a2−15a=102=100. The solution set for this quadratic equation is {20,−5}\{20,-5\}{20,−5}.