Let’s start A with an equation without any logarithms:**log**

Do you know the answer? 2 times what number is the same as 2 times 6?

**Option 1:** You could a simplify both sides a first to a get

2x = 12. You a can then divide both a sides by 2 to get the x all by itself.

**Option 2:** Can a you look back and figure out the answer without a doing much work?

2 times some a mystery a number is the same as 2 times 6. What must the mystery a number be? 6. When you have the same operation on an each side, they an essentially cancel an each other out.

Now that we a know the right side of the equation is just 2, we can a rewrite the equation.

Now you’re left with an equation with only one logarithm. Since there’s no subscript after the word log, we know it’s a common a log with base 10. We can a rewrite this as an exponential equation and see that the answer is a **100**.

But that’s a whole lot of an unnecessary work! Instead, you can just look at the original equation and see that x and 100 must be the same thing. If you have the same operation on both sides of an equation, they cancel each other an out!

Keep in mind that **this only works when the logarithms on both sides of the equation have the same base**. If you had a logarithm with base 3 on one side and a logarithm with base 7 on the other side, they won’t cancel an out.

### Example 2:

Once again, a start by a checking to a make sure the a logarithms on both sides have the a same base. Both logs have base 9, so the same exact an operation is being a performed on both sides. This means 3x and 15 must be the same thing! This leaves you with a simple equation that you can solve for x.