Writing logarithms in terms of r, s, and t with change of base

[terps]

Homework Statement

Let r = log9 31, s = log6 31, t = log9 6.

Write the following expressions in terms of r, s, and/or t. The change of base formula may be helpful in finding some of these logarithms.

Homework Equations

log 9 base 31

The Attempt at a Solution

I am not sure where to begin. I am confident with the different rules for logarithms such as log 5 + log 4 = log 20, but i am not sure how to switch bases. I am sure it has something to do with the equation r= log 31 base 9. All i am asking for is a little guidance.

 

[Mark44]

Does your book show the change-of-base formula?

 

[terps]

Yes it does, but i thought that you could only do that when they have common bases. what i mean is that you can only use it for example log 5/log 3 since they have the common base 10. No?

 

[Mark44]

The change-of-base formula can be used to change the base for any log expression with a reasonable base (base > 0, base != 1).

It's not clear to me what you need to do.

log 9 base 31

Get rid of "base" in there, and use subscripts to indicate the base.

I can't tell if this is supposed to be log₃₁ 9 or log₉31.

If the advanced menu bar isn't showing at the top of the input window, click Go Advanced. From the advanced menu, click the X₂ button, and it will add [ sub] [ /sub] tags, but without the leading spaces I show. The subscript should go between the two tags.

Similarly, you can get superscripts for exponents, by clicking the X² button. That button puts in [ sup] [ /sup] tags (again, without the spaces), and you enter the exponent between the two tags.

 

[terps]

Thank you for all of your help. I figured it out. the answer (per change of base formula) is log₉9/r. i was under the impression that we could only use the variables r s and t in our answer.