Laws of Exponents Let’s dig deep into our memories and try to remember the laws of exponents. Product Rule Quotient Rule It’s all coming back now. I remember this stuff.

Laws of Logarithms What are the Laws of Logarithms? Since Logarithms are just exponents written in a different form, maybe the Laws of Logarithms are the same as the Laws of Exponents. Product Rule Quotient Rule Power Rule This looks pretty easy, but how does it work with actual numbers?

Examples of the Logarithm Laws Product Rule Quotient Rule Power Rule May I press the easy button

Logarithm Laws in Action Express in terms of log m and log n I can do that. That one made my brain hurt, but I think I can do it.

More Logarithm Laws in Action If log 2 = x and log 3 = y, express each of the following in terms of x and y This really isn’t as difficult as I thought it was.

Solving Equations that Contain Logarithms That sounds confusing, but I guess I’ll give it a try. If log b A = log b B then A = B If log N = 2log x + log y solve for N in terms of x and y Try to put the equation in the form log b A = log b B Undo the power law log N = log x 2 + log y Undo the product law log N = log x 2 y Drop the log and set the numbers equal N = x 2 y

More Equations that Contain Logarithms Solve for x:x: Put the equation in the form log b A = log b B Undo the power law Undo the quotient law Drop the log and set the numbers equal Evaluate what you can Solve the equation

Exponentiating Logarithmic Equations Solve for x: Logarithms are exponents written in a different form Undo the product law Evaluate what you have Write in exponential form I’m not even sure what that means. You must check for extraneous roots Write your final answer x = 5x = 5 That looked hard at first, but it really wasn’t hard after all. Let’s give it a look.