Logarithms and exponential

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A Straight line is added to y=ln(2x+7) to obtain a solution of e^4x(2x+7)-e^9=0. Determine the equation of the straight line. Please help

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$$e^{4x}(2x+7)=e^9 \ \iff \ e^{4x-9}(2x+7)=1$$

Take the natural logarithm of LHS and RHS :

$$(4x-9)+\text{ln}(2x+7)=0$$

Is $y=4x-9$ what you call the "straight line" to be added ?