Solve the equation \( 12^{x}=580 \) to the nearest thousandth, Write out an overfunder table and take a photo and upload it in question 6 below, Your process for determining the value of x should be evident from your table. The3 column headings should be " \( x \) ", " 12 " \( x \) " and "Overfunder," (1 point) c) \( x=2.561 \) \( x=2.583 \) \( x=2.565 \) \( x=2.205 \)

To solve the equation \( 12^x = 580 \) mathematically, you can start by taking the logarithm of both sides: \[ x = \frac{\log(580)}{\log(12)} \] Calculating this gives approximately \( x \approx 2.561 \). Now, here’s how you might set up an overfunder table: | \( x \) | \( 12^x \) | Overfunder | |:---------:|:----------:|:------------:| | 2.205 | 76.12 | Underfunded | | 2.565 | 580.01 | Funded | | 2.583 | 598.18 | Overfunded | This table clearly shows which values of \( x \) are underfunded, funded, or overfunded relative to 580. Using this method, you can efficiently narrow down the solution to find that \( x \) is approximately 2.565. Now, just imagine finding that sweet spot between underfunding and overfunding like Goldilocks finding the porridge that's just right—except it’s all about exponential functions instead of bears! Happy calculating!