STEM Lessons for College Students

Solving Logarithmic Equations… How? (NancyPi)

MIT grad shows how to solve log equations, using LOG PROPERTIES to simplify and solve. To skip ahead: 1) For solving BASIC LOG EQUATIONS, skip to 0:22. 2) For ONE LOG ON EACH SIDE (EQUALITY property), skip to 2:36. 3) For TWO LOGS ADDED together and equaling a number (PRODUCT property), skip to 5:25. 4) For MANY LOGS, SUBTRACTED and ADDED, and using the QUOTIENT property, POWER property, and the other properties of logarithms (log rules), skip to 9:53. This video focuses on solving logarithms in equations and explains how to check the solution for an extraneous solution. Nancy formerly of MathBFF explains the steps.

For my video on logarithm basics like how to EVALUATE LOGS, including natural logs (ln x), jump to:

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SOLVING LOGARITHMIC EQUATIONS for x: Every logarithm is connected to an exponential form. The best way to figure out a log function is to REARRANGE THE LOG INTO EXPONENTIAL FORM and then solve for x. I show a quick recap of how to rewrite a log into exponential form, but for a longer explanation of rearranging into exponential form to evaluate a log, jump to my video “Logarithms… How?” ( for help with converting log to exponential form. In this video, I show you more complicated log equations with more than one log, where you’ll need the LOG PROPERTIES (logarithm rules) to simplify and be able to condense down to one logarithm on a side so that you can solve.

Solving logarithmic equations with LOGS ON BOTH SIDES: If you have one log on each side of the equation, with the same base, you can use the EQUALITY PROPERTY log formula.

If you have more than one log on a side of the equation (with the same base), you can use the PRODUCT PROPERTY (if the logs are added) or the QUOTIENT PROPERTY (if the logs are subtracted) to combine the logs into one log. If you have a number multiplied in front of a log, as a coefficient, you can use the POWER PROPERTY logarithm formula to bring the coefficient up as a power inside the log argument. Once you simplify the log equation using the product, quotient, and/or power properties, you can either 1) solve by using the equality property if you just have one log on each side (with same base), or 2) solve by rewriting into exponential form if you have a log on one side and a number on the other side. IMPORTANT – CHECK SOLUTIONS: When solving logarithmic functions, you have to CHECK your solutions for log equations. Any numbers you get as solutions you have to plug back into the original equation to check. If a solution does not work or gives an undefined value (for example: log of a negative number), then it is an “extraneous solution” and must be thrown out!

For more logarithm examples and help with solving logarithmic and exponential equations, logarithmic form problems, exponential function and exponential equation math, solving logarithmic expressions, solving log equations without a calculator, log x equations, exponential and logarithmic functions, exponent math, log solver and log equation solver math, log equations with the same base, and log equations with different bases, as well as more of my math videos for algebra, algebra 2, precalculus, and college algebra, check out:

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