Evaluate log_5 10 (Three significant digits.)

To evaluate log_5 10, we change the base from 5 to 10 using the change of base formula, log_b a = log_c a / log_c b. This gives us the calculation log_10 10 / log_10 5. The result is approximately 1.431 to three decimal places.

Explanation:

The question asks us to evaluate log_5 10 to three significant digits. This involves finding the power to which 5 needs to be raised to get 10. To find this, most calculators only have buttons for log base 10 and natural logs (base e), so we can use the change of base formula.

The change of base formula is log_b a = log_c a / log_c b. For this problem, we want to change the base from 5 to 10, so a=10, b=5, and c=10. Plugging in these numbers into the formula gives us log_10 10 / log_10 5.

Using your calculator, you can find that log_10 10 = 1, and log_10 5 ≈ 0.699. Dividing these values gives us approximately 1.431 to three decimal places, which is the approximate value of log_5 10.

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