5) Prove how the following equation is TRUE or FALSE.
[logb(x)]y = ylogb(x)
We believe that this is false.
If this was to be true, it would have to be:
logb(x)y = ylogb(x)
you need to remove the brackets for it to be equal.
FALSE
[logb(x)]y = ylogb(x)
let b=10, x=2, y=3
[log10(2)]3 = 3log10(2)
[log2/log10]3= 3log10(2)
0.027 = 0.903
this is obviously not correct.
TRUE
logb(x)y = ylogb(x)
ylogb(x) = ylogb(x)
This groups believes that because of the brackets, the equation is not correct and is a common error people can make. Since it's [logb(x)]y, you have to solve first and then put it to the power of 'y'.
If you don't agree with our solution, please post a comment on how you think it should be done. =)
be happy.
13 comments:
charlotte said...
I agree wid ur group Lindsay. The equation of: {sorry guys, i cant use the code for exponent in her, so bare with me} :[logb^(x)]^Y=Ylogb^(x) is false. because if u change the Equation into LN:
1.) [ln(x)/ln(b)]^Y=Y[ln(x)/ln(b)]
2.) you wanna get rid of the Y exponent of the left side of the equation:
Yln[ln(x)/ln(b)]=Y[ln(x)/ln(b)]
The equation are not equal, because when u look at the left side of the equation it contain a Extra LN and without it the equation would be equal.
If im wrong don't hesitate to correct me, i would gladly appreciate it!
GOOd JOb Gys!
I completely agree with your answer group 5. You removed the brackets so that the equation would equal each other. Therefore, the result would be the same. Super job!
i think i agree with your answer. you guys explained why the equation was false and that made it clear to me why. good job on coming up with a method on how to make it true. Awesome Job!!
i too agree with this group b/c in the original, equation, it had the square brackets[ ], which caused the equation to not equal each other. Removing the square brackets[ ]had therefore made the equation become equal and become TRUE! Your post really helped!!! ;)
too much color lol, its hard to read. Very simple solution to your question. i agree with your answer. State the rule you used to solve for your solution.
I agree that this equation is false. And also that it is true once the brackets are removed. It's an easy mistake to make, simple order of operations stuff. The kind of mistake I make about 5 zillion times a day. So good job guys, you're absolutely right.
I for one like the use of pretty colours, it makes learning easier and more fun to do =) I also agree that it is false. It makes sense that taking away the brackets would make it true. Your explanation is clear and easy to follow... awesome job guys =)
I agree with your answer because the square brackets on the true or false equation changes it by making the entire log have an exponent of Y which would make both sides of the equation come up with a different answer. As you said, if you take the square brackets out, the equation would be true.
I agree with your answer about it being false. When I look at problems like what Mr. K gave us, I think they look scary at first. but then if you just do what you guys did, then it's no prob. Simply removin the brackets fixed the problem. I think people would often make a mistake like that. Your explanation was very helpful and easy to understand.
The equation is false. I agree. The square brackets means that everything on the outside will be done to the inside. A logarithm is an exponent. You're having an exponent raised to an exponent. Not a power to an exponent. Therefore
[logb(x)]^y = y logb(x) is incorrect.
Good job guys! It's such a simple modification from the equation, but it makes all the difference in the world. Indeed when you take out the brackets, the expression holds true. I've made this mistake time and time again so I should know.
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