Use algebraic procedures to find the exact solution of the equation $\ln x = \frac { 1 } { 2 } \ln \left( 2 x + \frac { 19 } { 9 } \right) + \frac { 1 } { 2 } \ln 9$ .
A)-1, 19
B) $- \frac { 19 } { 14 }$
C)2, 9
D)19
E)1

Question

Quizplus · Accepted Answer

By using properties of logarithms, the equation can be rewritten as $\ln x = \ln \left( \sqrt{2x + \frac{19}{9}} \times 3 \right)$. Simplifying gives $x = 3\sqrt{2x + \frac{19}{9}}$. Solving this equation leads to the solution $x = 19$.

Use Algebraic Procedures to Find the Exact Solution of the Equation