How Do I Solve These Logarithmic Equations From My Math Exam?

  • Thread starter Procrastinate
  • Start date
In summary: So if you take logs of 0.95x = 3/2 0.90x , you get … ?xlog0.953/2x0.9 = xlog0.92/3x0.95xlog0.953/2x0.9 = xlog0.92/3x0.95
  • #1
Procrastinate
158
0
I had this question in the problem solving part of my Maths Exam. When I extrapolated all the critical information from the question, I narrowed it down to this equation. However, I just couldn't solve the equation. Could anyone please help? This has been bugging me for the whole day.


y = 2000 x 0.95^x - equation 1
y = 3000 x 0.90^x - equation 2
 
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  • #2
Hi Procrastinate! :smile:

(try using the X2 tag just above the Reply box :wink:)
Procrastinate said:
y = 2000 x 0.95^x - equation 1
y = 3000 x 0.90^x - equation 2

So 0.95x = 3/2 0.90x …

ok, now take logs. :smile:​
 
  • #3
tiny-tim said:
So 0.95x = 3/2 0.90x …

Wouldn't that be log 0.95 3/20.9x = x

That's what I did, but the fact that there was an x still in the index was what hindered me from completing it.
 
  • #4
Procrastinate said:
Wouldn't that be log 0.95 3/20.9x = x

That's what I did, but the fact that there was an x still in the index was what hindered me from completing it.

ah … you need this equation …

keeping to the same base, a, what's loga(b2) ?

and what's loga(bc) ? :smile:​
 
  • #5
tiny-tim said:
ah … you need this equation …

keeping to the same base, a, what's loga(b2) ?

and what's loga(bc) ? :smile:​

Sorry, but I am still a bit confused about the notation. Do I square it first and then do loga(bc)?
 
  • #6
Procrastinate said:
Sorry, but I am still a bit confused about the notation. Do I square it first and then do loga(bc)?

They're two separate questions …

I thought I'd start you off with an easy one first …

what's loga(b2) ?
 
  • #7
tiny-tim said:
They're two separate questions …

I thought I'd start you off with an easy one first …

what's loga(b2) ?

2logab
 
  • #8
(just got up :zzz: …)

Yup! :smile:

Now what's loga(bc) ? :wink:
 
  • #9
clogab
 
  • #10
Yes!

So if you take logs of 0.95x = 3/2 0.90x , you get … ? :smile:
 
  • #11
xlog0.953/2x0.9 = xlog0.92/3x0.95
 
  • #12
Procrastinate said:
xlog0.953/2x0.9 = xlog0.92/3x0.95

I'm not following that at all :confused:

This is supposed to be taking logs of 0.95x = 3/2 0.90x …

take them in the same base (preferably 10 :wink:).
 

FAQ: How Do I Solve These Logarithmic Equations From My Math Exam?

What is a log or index in scientific research?

A log or index in scientific research is a record-keeping system that documents all the details of an experiment or study. It includes information such as the date, time, materials used, procedures followed, and results obtained.

Why is it important to keep a log or index?

A log or index is important because it helps scientists keep track of their research process and results. It also serves as a reference for future studies and allows others to replicate or build upon the research.

How do I create a log or index for my research?

To create a log or index, you should first determine what information is important to record. Then, choose a format that works best for you, whether it's a notebook, spreadsheet, or electronic database. Be consistent in recording information and make sure to date each entry.

What should I include in my log or index?

Your log or index should include details about your research process, such as the purpose of the study, materials used, methods and procedures, observations, and results. It should also include any unexpected events or changes made during the research.

Can I use someone else's log or index for my own research?

No, it is not recommended to use someone else's log or index for your own research. Each study is unique, and using someone else's log may not accurately reflect your own research process. It is best to create your own log or index to ensure accuracy and consistency in your research.

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