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 + 3) - log(2x) = [log(x + 3)/log(2x)]

Accepted Answer

Hey everyone in this problem we are asked to verify if the given equation is true and then if it's false whereas to make the necessary changes to amend that equation and make it true. Okay so we're given a log of two X plus seven minus log of five X. Is equal to log of two X plus seven divided by log of five X. So let's start with the left hand side of this equation and see if we can get it to write it as the right hand side to see if that statement is true or false. So we have log of two X plus seven minus log of five X. Now let's recall our log rule for dealing with the subtraction of two. Looks if we have log base B of something we can call em and we subtract log base B of something called N. We can write this as log base B of M divided by. So if we subtract two logs with the same base, we can write this as one single log where we're divide the arguments of those two separate logs we had subtracted. So if we apply this to our problem we get log the same base in this subtraction. K. Each log has the same base. So we leave that same base and inside our log we're gonna have the argument of the first thing, the argument of that. First log two X plus seven and then we're going to divide it by the argument of the log that gets subtracted. So we're gonna divide by five X. So now we have log of two X plus 7/5 X. And what you'll notice is that this does not equal log of two X plus seven divided by log of five X. And we only have one single log with those two things divided inside of our log. Okay? So our statement is false and the true statement is the one that we've just written. So log of two X plus seven minus log of five X. Is equal to log two X plus 7/5 X. And that's going to be option B. So the answer here is be that original statement is false and we found the correct statement. Thanks everyone for watching. I hope this video helped see you in the next one.

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 + 3) - log(2x) = [log(x + 3)/log(2x)]

Key Concepts

Properties of Logarithms

Logarithmic Equations

True and False Statements in Mathematics

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