The largest integer n𝑛 for which 0.6n0.6𝑛 is less than 1717 is

The question is asking for the largest integer n for which 0.6^n is less than 17.

Here are the steps to solve this problem:

Step 1: Set up the inequality 0.6^n < 17

Step 2: To make the problem easier to solve, take the natural logarithm (ln) of both sides. This is because the logarithm of a number to a certain base is the exponent to which the base must be raised to produce that number. In this case, we want to find the exponent (n) for the base (0.6). ln(0.6^n) < ln(17)

Step 3: Use the power rule of logarithms to bring down the exponent. The power rule states that the logarithm of a number raised to an exponent is equal to the exponent times the logarithm of the number. n * ln(0.6) < ln(17)

Step 4: Solve for n by dividing both sides by ln(0.6). n < ln(17) / ln(0.6)

Step 5: Calculate the value of the right side using a calculator. n < 22.46

Since n has to be an integer, we round 22.46 down to get the largest integer less than 22.46.

So, the largest integer n for which 0.6^n is less than 17 is 22.