Question

Solve for x. Round all answers to the nearest hundredths

Answer 1

The solution to
`\(2 \cdot \log_9(7) - (1)/(2) \cdot \log_9(x) = 2 \cdot \log_9(6.3)\)` is
`\(x \approx 1.52\)`, rounded to the nearest hundredths.

To solve the equation
`\(2 \cdot \log_9(7) - (1)/(2) \cdot \log_9(x) = 2 \cdot \log_9(6.3)\)` for x, follow these steps:

1. Combine the logarithmic terms on one side:

`\[2 \cdot \log_9(7) - 2 \cdot \log_9(6.3) = (1)/(2) \cdot \log_9(x)\]`

2. Use the properties of logarithms to simplify:

`\[\log_9\left((7^2)/(6.3^2)\right) = \log_9(x^(1/2))\]`

3. Set the arguments equal to each other:

`\[(7^2)/(6.3^2) = x^(1/2)\]`

4. Solve for x:

`\[x = \left((7^2)/(6.3^2)\right)^2\]`

Now, calculate the value of x:

`\[x \approx \left((49)/(39.69)\right)^2 \approx 1.52646\]`

Rounded to the nearest hundredths,
`\(x \approx 1.52\)`.