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.

[log(x + 2)/log(x - 1)] = log(x + 2) - log(x - 1)

Accepted Answer

Hey everyone welcome back in this problem. We are asked to verify if the given equation is true. Okay and if the equation or the statement is false, were asked to make changes to the equation to make it true and the expression or the equation we're given is log of eight x plus 13 divided by log of three x minus one is equal to log of eight x plus 13 minus log of three x minus one. Okay well if we look at this on the left hand side we're dividing two different logs. Okay now we have a property that allows us to deal with division within log. The only property we have that deals with division of logs is the change of base. Okay. And that inside of one of these logs is gonna become the base. We don't want to have X in our base. Okay? That's not what we're looking for. That's not going to give us the right hand side. So let's start with the right hand side of the equation instead. So the right hand side of the equation is log of eight x plus 13 minus log of three x minus one. Now recall a property for dealing with the subtraction of two logs with the same base. If we have log base B of em minus log base B of N. The property tells us that we can write this as log base B of M divided by N. So we keep the same base and the subtraction becomes a division within one single log applying this to our expression, we're going to get log of the first term eight x plus 13 divided by the term being subtracted, the re x minus one. Okay, so this is a true statement here. The statement we were given is false. We don't have the division of two logs. We have the division of two terms within a single log. So the answer is b false. And the correct statement is that statement we've just written log of eight x plus 13 divided by three x minus one is equal to log of eight x plus 13 minus log of three x minus one. That's it for this one. Thanks everyone for watching.

My Courses

Chemistry

Biology

Math

Physics

Business

Social Sciences

Programming

Product & Marketing

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. [log(x + 2)/log(x - 1)] = log(x + 2) - log(x - 1)