Solving an exponential equation by taking the log of both sides

👉 Learn how to solve exponential equations. An exponential equation is an equation in which a variable occurs as an exponent. To solve an exponential equation, we isolate the exponential part of the equation. Then we take the log of both sides. Note that the base of the log should correspond to the base of the exponential part of the equation, so that the log cancels out the exponential function, leaving out only the exponent.

If we can make the base of both sides of the equation to be equal, we then equate their respective exponents and then solve.

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[brianmclogan]

log base 3 of three is equal to one, so as long as you take the log base three one both sides you produce equivalent equations. In other words I took the log of base three to both sides. Its okay because I did it to both sides. I choose to take the log of base 3 because it would only leave me x on the left side, therefore allowing me to solve for my variable

[Maluras]

Accidently stumbled across the log definition "proof" I needed! Thanks :)

[AshleyHillebold]

thank you! this helped a lot. i couldn't figure out that you had to change the base of the log when you log both sides until now

[GreaterDeity]

Hey don't get frustrated bro! Remember that your students haven't been studying math as long as you. They might be having the same road blocks that you used to have a long time ago. So, just be patient with them. I still don't quite understand logarithms myself! :(

[PopaDom]

What about X^3/4 = 2? How do I solve it?

[cloudenvying]

this guy's doing a pretty good impression of Kraftwerk's The Man Machine cover.

[GreaterDeity]

What's the process behind getting that log3 in the denominator: I am not catching that one.