Final answer:
To find the domain of a log function using a calculator, only positive numbers can be entered, as logarithms are undefined for zero and negative values. You can calculate the inverse using the 10x or INV log function after entering the negative of the value (e.g., pH). For natural logarithms, use the ln button and its inverse function ex accordingly.
Step-by-step explanation:
To find the domain of a log function, you will need to understand that a logarithm function is defined only for positive real numbers. Therefore, when you're using a calculator to find the logarithm of a number, you can only enter positive values. The natural logarithm (ln) button is used for base e logarithms, while the LOG button is used for common base 10 logarithms. When dealing with equations involving inverses, such as when calculating the pH from a given [H3O+], you may use the inverse log function. This is typically accessed by using your calculator's second function key combined with the log button. For instance, to find the concentration of hydronium ions ([H3O+]) in a solution with a pH of 8.3, you negative the pH value and then use the inverse function typically labeled as 10x or INV log.
- Enter 8.3 as a negative number using the +/- key.
- Access the inverse log function (10x or INV log) either by using the second function key or directly if available.
- The calculator will then display the concentration of hydronium ions, which should be 5.0 × 10-9 M.
It's important to remember that for the natural logarithm of a number, you use the ln button. To calculate a number from its natural logarithm, you take the inverse ln of the number or calculate ex where x is the natural logarithm of the number.