Learn about the properties of logarithms that help us rewrite logarithmic expressions, and about the change of base rule that allows us to evaluate any logarithm we want using the calculator.
Learn how to rewrite any logarithm using logarithms with a different base. This is very useful for finding logarithms in the calculator!
Sal explains what logarithms are and gives a few examples of finding logarithms. Created by Sal Khan.
Logarithms are the inverses of exponents. They allow us to solve challenging exponential equations, and they are a good excuse to dive deeper into the relationship between a function and its inverse.
There are a few rules you want to know for calculations involving logarithms like pH and pOH . For a review of log properties, see Sal's video on properties of logarithms .
Think of it this way -- logarithms are just another way of looking at things. You know that 2^3 is 8, but if you didn't know what power to raise it to, you'd say 2^x is 8.
So this is a logarithm property. If I'm taking the logarithm of a given base of something to a power, I could take that power out front and multiply that times the log of the base, of just the y in this case.
We can calculate the pH of a solution by taking the negative logarithm of the hydronium ion concentration, or pH = -log [H₃O⁺]. At 25°C, a solution with pH < 7 is acidic, a solution with pH > 7 is.
