Evaluate the given logarithm using the change of base formula and a calculator. Use the common log. log ⁡ 3 17 \log_317 lo g 3 17

In this problem, we're asked to evaluate the given log using the change of base formula and a calculator. And here we wanna use common logs. Now we're given log base 3 of 17, and we wanna change this to base 10 logs, the common log. So let's go ahead and do that here. Now log base 3 of 17 using my change of base formula, I start with my common logs on both the top and bottom of a fraction. And I know that this 17 is going to go on the top so this is log of 17 and then 3 my base will go on the bottom remember base bottom so this becomes a log of 17 over log of 3. Now that I have this, I can go ahead and just plug this into my calculator all at once using that log button. So log 17 divided by log 3. Make sure you're using parentheses wherever you feel that they're needed, and you're going to get about 2.58. You're gonna get a longer decimal, but rounding this, we get 2.58, and that is our final answer. Thanks for watching, and let me know if you have questions.