Understanding Logarithms: Solving Equations and Creating Tables of Values

[ohhnana]

Homework Statement

Ok I'm taking an online advanced function course, and we are on logarithms and I don't get it one bit , there two questions given to me 1. y = 2 log10x and y = log5 (x – 2),

Homework Equations

The told me to make a table of value , i don't understand how i will get the numbers,
can and explain how i would be able to solve this

The Attempt at a Solution

 

[danago]

Besides using approximations, i think you will just need to use a calculator to evaluate logarithms. I'm assuming that the 10 and the 5 after 'log' refer to the base of the logarithm? Some calculators might only have base 10 logarithms and base e logarithms (natural logarithm), so to evaluate a base 5 log you will need to change the base. If this is the case then do a google search for 'logarithm change of base'

 

[ohhnana]

so what does the 2 before the log mean, i get the base part and stuff

 

[danago]

Well as you have written it just looks like it is 2 multiplied by the logarithm.

 

[symbolipoint]

You are trying to jump too many courses. The earliest course in which you learn about logarithms is "Algebra 2" (Intermediate Algebra). The functions learned there are not advanced. The course and topic progression could go something like this:

Algebra 1 - learn about numbers, mostly Real numbers. Learn about points and lines on cartesian coordinate system.
Algebra 2 - learn about number functions; learn about inverses of functions. In particular, you study exponential functions and their inverses, the logarithmic functions.

You showed us this:

there two questions given to me 1. y = 2 log10x and y = log5 (x – 2),

Are you trying to express these?
$$\[ y = 2\log (10x) \]$$ and $$\[ y = \log (5(x - 2)) \]$$


If so, then what is the base supposed to be?

Or are you trying to express these:
$$\[ y = 2\log _{10} x \]$$ and $$\[ y = \log _5 (x - 2) \]$$
?

 

[HallsofIvy]

"Make a table of values" means to evaluate them for different values of x- and you will need a calculator to do that. Logarithm to base 10 will be on your calculator, probably a key labled "LOG" (as opposed to LN which is a different kind of logarithm). To find the logarithm to base 5, use the formula
$$log_a(x)= \frac{log_{10}(x)}{log_{10}(a)}$$
with a= 5.

 

[eumyang]

"Make a table of values" means to evaluate them for different values of x- and you will need a calculator to do that. Logarithm to base 10 will be on your calculator, probably a key labled "LOG" (as opposed to LN which is a different kind of logarithm). To find the logarithm to base 5, use the formula
$$log_a(x)= \frac{log_{10}(x)}{log_{10}(a)}$$
with a= 5.

If you have a TI-84 with a recent version of its OS, however (at least 2.53MP), you can take the logarithm with any base without needing to use the change of base formula.

Really cool, I think.

 

[ohhnana]

Thank you very much , I'm starting to understand this more .. i have a TI-84 plus how do i get the recent version of OS?

 

[eumyang]

Thank you very much , I'm starting to understand this more .. i have a TI-84 plus how do i get the recent version of OS?

Here is the most recent OS file:
http://education.ti.com/calculators/downloads/US/Software/Detail?id=6014"

In order to download it to your calculator you will need TI-Connect...
Windows: http://education.ti.com/calculators/downloads/US/Software/Detail?id=183"
Mac: http://education.ti.com/calculators/downloads/US/Software/Detail?id=286"

... and a USB cable.