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Were asked to simplify log base 3 of 27x. And frankly, this is already quite simple. But Im assuming they want us to use some logarithm properties and manipulate this in some way, maybe to actually make it a little bit more complicated. But lets give our best shot at it. So the logarithm property that jumps out at me-- because this right over here-- were saying what power do we have to raise 3 to to get 27x? 27x is the same thing as 27 times x. And so the logarithm property it seems like they want us to use is log base-- let me write it-- log base b of a times c-- Ill write it this way-- log base b of a times c. This is equal to the logarithm base b of a plus the logarithm base b of c. And this comes straight out of the exponent properties that if you have two exponents, two with the same base, you can add the exponents. So let me make that a little bit clearer to you. And if this part is a little confusing, the important part for this example is that you know how to apply this.
