![]() You could plug it into your calculator figure out 7³ or you could just leave it in this form as well.Ĭondensing a bunch of logs and also dealing with a constant term, all you need is to turn the constant term into the same log, just typically by doing log base, base of the same number that you’re already dealing with. Use the product property of logarithms, logb(x)+ logb(y) logb(xy) log b ( x) + log b ( y) log b ( x y). log2(x3)log2((x+3)4)+log2 (y) log 2 ( x 3) - log 2 ( ( x + 3) 4) + log 2 ( y) Use the quotient property of logarithms, logb (x. ![]() Now we are adding which corresponds to multiplication so we can take this 7³ and bring it into the same log, leaving us with log base 7, 7³, x² over y to the third. 3log2 (x) 4log2 (x + 3) + log2 (y) 3 log 2 ( x) - 4 log 2 ( x + 3) + log 2 ( y) Simplify each term. This is the same exact thing as 3 so we just this term into a log term. So 3 is actually 3 times log base 7 of 7.ĭoing the same thing we did over here with our coefficient w can bring that up around and so now we have log base 7 of x² over y³ plus log base 7 of 7³. Logarithmic Expansion takes place when we convert a logarithm into multiple logarithms using the properties of logarithms. So what we could say then is this is equal to 1, we multiply 1 by 3 and we get 3. In this lesson, you’ll be presented with the common rules of logarithms, also known as the log rules. log(x) 21log(y)+4log(z) Enclose arguments of functions in parentheses and include a multiplication sign between terms. Remember if the base and what’s inside the log are the same thing, it’s going to be equal to 1. Transcribed image text: Condense the expression to a single logarithm using the properties of logarithms. Which of the following is another way to express. We know that log base 7 of 7 is equal to 1. Express the following in condensed form: log(x2)+log(y2) Same. What we can have is we need a log 7, log base 7 term associated with that. The following properties serve to expand or condense a logarithm or logarithmic expression so it can be worked with. Whenever we’re combining logs we need to have the same base, so we somehow need to be able to write three as a log base 7. The problem is that we somehow, we don’t have any log to bring this into this statement. ![]() I still want to get this plus three into this log so I just have one statement. The subtraction always turns into division so we end up with log base 7 of x² over y³ and then we’re still left with this plus three. The first thing we have to do is bring our coefficients up to the numerator so we end up with log base 7 of x² minus log base 7 of y to the third and our plus 3 is still hanging out at the end. The first two can be condensed using the quotient rule. For this particular example what we’re going to do is condense these three terms down into a single log. ![]() Using laws of logarithms to condense a bunch of logs. ![]()
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