Solve the logarithmic equation below algebraically. Round your result to three decimal places.
$$\log _ { 9 } 4 x - \log _ { 9 } ( 1 + \sqrt { x } ) = 2$$
A) $449.651$
B) $618.792$
C) $849.024$
D) $5.103$
E) $161.208$

Question

Quizplus · Accepted Answer

Using the properties of logarithms, the equation can be simplified and solved for $x$. First, combine the logarithms on the left side using the quotient rule: $\log_9 \frac{4x}{1 + \sqrt{x}} = 2$. Then, convert the logarithmic equation to its exponential form: $9^2 = \frac{4x}{1 + \sqrt{x}}$. Solving this equation for $x$ gives $x = 449.651$.

Solve the Logarithmic Equation Below Algebraically log⁡94x−log⁡9(1+x)=2\log _ { 9 } 4 x - \log _ { 9 } ( 1 + \sqrt { x } ) = 2log9​4x−log9​(1+x​)=2

Solve the Logarithmic Equation Below Algebraically $\log _ { 9 } 4 x - \log _ { 9 } ( 1 + \sqrt { x } ) = 2$