Question

The sum of all the solutions to the equation $7^{3x^2}\cdot 5^x=11$, is

• A. $\ln 5$
• B. ${\log }_{5}7$
• C. $\frac{\ln (1/5)}{\ln 7}$
• D. none

Answer 1

Answer: (D)

Given $7^{3x^2}\cdot 5^x=11$
taking $\log 3x^2\ln 7+x\ln 5=\ln 11$
$\Rightarrow (3\ln 7)x^2+(\ln 5)x-\ln 11=0$
sum $=\frac{-\ln 5}{3\ln 7}$