Ex

[djens1342]

Hey everyone, I seem to be confusing myself with this problem.
“If Logb(5)=2.007 and Logb(9)=2.74 then what is the value of Logb(1/sqrt45)”
I’d assumed the equation -1/2 (2.74-2.007) would work however it’s just not clicking for me right now. Thanks

 

[Deleted member 4993]

Hey everyone, I seem to be confusing myself with this problem.
“If Logb(5)=2.007 and Logb(9)=2.74 then what is the value of Logb(1/sqrt45)”
I’d assumed the equation -1/2 (2.74-2.007) would work however it’s just not clicking for me right now. Thanks

Use:

log(x)^(1/2) = 1/2 * log(x)...........and

log(x*y) = log(x) + log(y)

Start from Log_b(1/sqrt45) and try to re-write it so that you can use the above properties.

 

[Dr.Peterson]

Hey everyone, I seem to be confusing myself with this problem.
“If Logb(5)=2.007 and Logb(9)=2.74 then what is the value of Logb(1/sqrt45)”
I’d assumed the equation -1/2 (2.74-2.007) would work however it’s just not clicking for me right now. Thanks

You're very close!

Just write out the details of your work, and particularly look for sign errors.

If you don't find the error, then show us the work so we can help you see it.

 

[JeffM]

[math]log_b(5) = 2.007 \text { and } log_b(9) = 2.74 \implies log_b(45) = \text {WHAT?}[/math]

 

[Steven G]

As JeffM pointed out, you need to 1st figure out what log_b(45) equals?

 

[Cubist]

[imath]\log_b(5) = 2.007 \text { and } \log_b(9) = 2.74 \implies [/imath] their calculator rounds numbers to 4 decimal places

 

[JeffM]

@Cubist

Apparently, the problem does not ask the student to determine b, but just to determine a numeric value (approximate or exact is unclear) for

[math]log_b \left ( \dfrac{1}{\sqrt {45}} \right )[/math]
The issue then is one of basic log rules rather than precision (as Dr. P hinted). I am not sure whether the student misunderstood the problem or simply made a simple mistake.

 

[Harry_the_cat]

Use:

log(x)^(1/2) = 1/2 * log(x)...........and

log(x*y) = log(x) - log(y)

- should be + on last line.

 

[Harry_the_cat]

Hey everyone, I seem to be confusing myself with this problem.
“If Logb(5)=2.007 and Logb(9)=2.74 then what is the value of Logb(1/sqrt45)”
I’d assumed the equation -1/2 (2.74-2.007) would work however it’s just not clicking for me right now. Thanks

Why are you subtracting in the brackets?

 

[Cubist]

@Cubist

Apparently, the problem does not ask the student to determine b, but just to determine a numeric value (approximate or exact is unclear) for

[math]log_b \left ( \dfrac{1}{\sqrt {45}} \right )[/math]
The issue then is one of basic log rules rather than precision (as Dr. P hinted). I am not sure whether the student misunderstood the problem or simply made a simple mistake.

I just think something like, "Using these approximations" would have been a more appropriate way of phrasing the question. Especially because it said, "do not round your answer", although that's probably done because it's an online question/ answer site that expects the answer in a certain way. Sometimes I can be a bit too logical. Like, they might as well say if x=3 and x=4 then... ?

 

[Steven G]

log(x*y) = log(x) - log(y)

@Subhotosh Khan
You get some corner time for that error.

 

[Deleted member 4993]

@Subhotosh Khan
You get some corner time for that error.

And I am off to the cool & dark corner.

 

[JeffM]

I just think something like, "Using these approximations" would have been a more appropriate way of phrasing the question. Especially because it said, "do not round your answer", although that's probably done because it's an online question/ answer site that expects the answer in a certain way. Sometimes I can be a bit too logical. Like, they might as well say if x=3 and x=4 then... ?

No one ever said I was logical. Long, long ago, when I used to write code and the computer would misbehave, I’d say what kind of illogic could I have dreamed up to confuse the poor machine that way. It seldom took me long to find what inanity had jumped full formed like Athena from Zeus’s head. Confusion ranges free in my head. It has been the secret of my success. It is especially valuable during negotiations.

 

[Cubist]

It seldom took me long to find what inanity had jumped full formed like Athena from Zeus’s head. Confusion ranges free in my head.

It has been the secret of my success. It is especially valuable during negotiations.

Together, as a team of tutors, I think we've got all the bases covered! (pun intended!)