In Exercises 89–102, determine whether each equation is true or f...

Question

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement.log6 [(x - 1)/(x^2 + 4)] = log6 (x - 1) - log6 (x^2 + 4)

Accepted Answer

everyone in this problem. We are asked to verify if the given equation is true and to make necessary changes to support the conclusion and amend the equation if this statement is false. Alright so the statement we're given is log base five of seven x minus two. All divided by two X squared plus five is equal to log base five of seven x minus two minus log base five of two X squared plus five. Let's go ahead and start with the left hand side of the expression. Log base five of seven X minus two, divided by two X squared plus five. Well let's recall. We have division within our log we have a rule a log property that allows us to deal with this. That log property tells us that if we have log base B have something say X divided by Y. This can be written as log base B. Of x minus log base B. Okay, so the division within a log becomes the subtraction of two logs with the same base Applying this to our expression. We have base five. So the base of our new logs will be five. We're going to get log base five K. Of the numerator, seven x minus two minus log base five of the denominator two, X squared plus five. Okay and if you look that is actually equal to the expression on the right hand side. Okay so the left hand side does equal the right hand side. So this statement is in fact true. Thanks for watching everyone. See you in the next video

Struggling with College Algebra?

In Exercises 89–102, determine whether each equation is true or false. Where possible, show work to support your conclusion. If the statement is false, make the necessary change(s) to produce a true statement.log6 [(x - 1)/(x^2 + 4)] = log6 (x - 1) - log6 (x^2 + 4)

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