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  4. The sum of all the solutions to the equation 73 x2 ⋅ 5x=11, is

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

Continuity and Differentiability

Solution:

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