# Help with Logarithms: Expressions in Terms of r, s, & t

• terps
In summary, the conversation was about using the change-of-base formula to write expressions in terms of r, s, and t, which were defined as log9 31, log6 31, and log9 6 respectively. The formula can be used for any log expression with a reasonable base, and it was used to change the base of log9 31 to log99/r. The conversation also discussed using subscripts and superscripts for bases and exponents in equations.

## 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.

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.

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

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?

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.
terps said:
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.

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.

## 1. What is a logarithm?

A logarithm is an operation in mathematics that represents the power or exponent to which a fixed number, called the base, must be raised to produce a given number.

## 2. How do I write a logarithm expression in terms of r, s, and t?

To write a logarithm expression in terms of r, s, and t, you need to identify the base of the logarithm and the number being raised to that power. Then, you can use the properties of logarithms to rewrite the expression in terms of r, s, and t.

## 3. What are the properties of logarithms?

The properties of logarithms include the product rule, quotient rule, power rule, and change of base rule. These rules allow you to manipulate and simplify logarithmic expressions.

## 4. How can I solve logarithmic equations?

You can solve logarithmic equations by using the properties of logarithms to rewrite the equation in a simpler form. Then, you can solve for the variable using algebraic techniques.

## 5. Why are logarithms important in science?

Logarithms are important in science because they are used to represent and manipulate exponential growth and decay. They are also used to compare quantities that vary over several orders of magnitude, making them useful in fields such as biology, chemistry, and physics.