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The equation y equals 16 times natural log x plus 31 relates a dog's age in years to the corresponding human age in years, where x equals the dog age and y equals the human age. Number one, if a dog is two years old, how old is a dog in human years? Round to 1/10 of a year. So here we are given x, the dog age. We want to find y, the corresponding human age, where y is equal to 16 times natural log of x when our case x is two. So we have natural log two plus 31. And now we go the calculator and get a decimal approximation. We enter 16, click functions, click ln for natural log. Go back to the main menu, click two, close parenthesis. Plus 31, rounding to the tenths place value or one decimal place. We round up because of the nine in the second decimal place or the hundreds place value. We have approximately 42.1. We now know a two year old dog is approximately 42.1 years old in human years. Number two, how old is a dog if it is 65 in human years? Again, round to 1/10 of a year. So here are given y, the corresponding human age, we want to find x, the dog age. So to set this up, we substitute 65 for a y, which gives us 65 is equal to 16 times natural log x plus 31. To solve this log equation, we first isolate natural log x and then write the log equation as an exponential equation, using the definition shown here in the lower right-hand corner. So we first subtract 31 on both sides. 65 minus 31 is equal to 34, giving us 34 is equal to 16 times natural log x. The next step is to divide both sides by 16, simplifying on the right 16 divided by 16 simplifies the one, giving us natural log x is equal to 34/16, which does simplify because 34 and 16 share a common factor of two. 34/16 simplifies to 17/8. And we can check this on the calculator by entering 34, divided by 16 enter and then click the convert to fraction button here on the right, which does give us 17/8. Now that we have the natural log of x isolated, we write the log equation as an exponential equation. Remember, natural log is log base e. So e is the base. 17/8 is the exponent and the number is x. We're working our way around the equal sign. We have e raised to the power of 17/8 is equal to x. And now we go back to the calculator to get a decimal approximation for x, the dog's age. We go back to functions. e is toward the bottom, and then we hit the exponent key, which is a to the power of b. Then enter the fractional exponent of 17/8 and go back to the main menu or...