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When the bases are the same, or the exponents are the same, you can just compare the parts that are different. Logarithmic equations may also involve inputs where the variable has a coefficient other than 1, or where the variable itself is squared.
I start with the original equation and work with the "outer" log: You can use the Mathway widget below to practice solving logarithmic equations (or skip the widget and continue with the lesson).
Try the entered exercise, or type in your own exercise.
This will be important down the road and so we can’t forget that.
Now, let’s start off by looking at equations in which each term is a logarithm and all the bases on the logarithms are the same.
to solve equations using the change-of-base formula, or always by using the definition of logs, or any other particular method.
But I am suggesting that you should make sure that you're comfortable with the various methods, and that you shouldn't panic if you and a friend used I can't do anything with this equation yet, because I don't yet have it in the "log(of something) equals a number" form.
So I'll need to use log rules to combine the two terms on the left-hand side of the equation: Now the equation is arranged in a useful way.
At this point, I can use The Relationship to convert the log form of the equation to the corresponding exponential form, and then I can solve the result: Keep in mind that you can always check your answers to any "solving" exercise by plugging those answers back into the original equation and checking that the solution "works".
When you have solved other algebraic equations, you often relied on the idea that you can change both sides of the equation in the same way and still get a true equation.
This is true with logarithms, too: If x = y, then log Another kind of exponential equation has exponential expressions on both sides.