Determine whether the value x=729 is a solution of the equation $\log _ { 9 } ( 7 x ) = \frac { 3 } { 2 }$ .
A)not a solution
B)solution

Question

Quizplus · Accepted Answer

To determine if $x=729$ is a solution, substitute $x$ into the equation: $\log_9(7(729)) = \frac{3}{2}$. Simplify the inside of the logarithm: $7(729) = 5103$. The equation becomes $\log_9(5103) = \frac{3}{2}$. The right side, $\frac{3}{2}$, suggests that $9^{\frac{3}{2}}$ should equal the argument of the logarithm for the equation to hold true. However, $9^{\frac{3}{2}} = (9^1)^{\frac{3}{2}} = 9^{1 \cdot \frac{3}{2}} = 9^{\frac{3}{2}} = 27$, which is not equal to 5103. Therefore, $x=729$ is not a solution to the given equation.

Determine Whether the Value X=729 Is a Solution of the Equation