# Logarithm question.

## Homework Statement

"If log3m = n, then determine log3m4, in terms of n."

2. The attempt at a solution

I'm pretty much clueless as how to set up the equation, and what 'in terms of n' means. My guess is log3m = log3m4, but I'm confused about what to do next. The answer in the textbook says 4n, and this leads me to believe that you take out the exponent from log3m4 but I'm not sure how you would do this.

Thanks.

Dick
Homework Helper

## Homework Statement

"If log3m = n, then determine log3m4, in terms of n."

2. The attempt at a solution

I'm pretty much clueless as how to set up the equation, and what 'in terms of n' means. My guess is log3m = log3m4, but I'm confused about what to do next. The answer in the textbook says 4n, and this leads me to believe that you take out the exponent from log3m4 but I'm not sure how you would do this.

Thanks.

Weren't you given some rules of logarithms like log(a^b)=b*log(a)?

Weren't you given some rules of logarithms like log(a^b)=b*log(a)?

Nope, my class was only told exponential form and logarithmic form, no rules of logarithms so far. We're only on the first part of the logarithm unit, the question above is a part of the "Extend" section of the chapter, which thought provoking questions than the others.

Dick
Homework Helper
Nope, my class was only told exponential form and logarithmic form, no rules of logarithms so far. We're only on the first part of the logarithm unit, the question above is a part of the "Extend" section of the chapter, which thought provoking questions than the others.

Ok, that's fair. So log_3 m=n means 3^n=m. So m^4=(3^n)^4. What does the exponential form tell you about that?

Ok, that's fair. So log_3 m=n means 3^n=m. So m^4=(3^n)^4. What does the exponential form tell you about that?

So log_3 m=n means 3^n=m.

- I understand this part.

m^4=(3^n)^4

- this confuses me a bit, since there's a fourth power on both sides.

I thought log_3 m^4 = n was: 3^n = m^4.

Dick
Homework Helper
So log_3 m=n means 3^n=m.

- I understand this part.

m^4=(3^n)^4

- this confuses me a bit, since there's a fourth power on both sides.

I thought log_3 m^4 = n was: 3^n = m^4.

That's a good start. But I'm having a hard time understanding the problem on the second. If a=b then a^4=b^4, yes?

That's a good start. But I'm having a hard time understanding the problem on the second. If a=b then a^4=b^4, yes?

I'm having trouble understanding the exponent part.

In this situation a≠b. Adding the forth power to (3^n) changes the equation. Maybe if I rewrite log_3 m^4 as log_3(m^4) might help. I'm confused as to how you move the exponent. The way I think of it is, the exponent moves with the variable m.

Sorry if you're having trouble understanding my problem :x.

Dick
Homework Helper
I'm having trouble understanding the exponent part.

In this situation a≠b. Adding the forth power to (3^n) changes the equation. Maybe if I rewrite log_3 m^4 as log_3(m^4) might help. I'm confused as to how you move the exponent. The way I think of it is, the exponent moves with the variable m.

Sorry if you're having trouble understanding my problem :x.

You are having some serious conceptual problems here. You've already agreed that 3^n=m. How can it not be that (3^n)^4=m^4? This part isn't about logs.

You are having some serious conceptual problems here. You've already agreed that 3^n=m. How can it not be that (3^n)^4=m^4? This part isn't about logs.

Since I'm having serious conceptual problems, can you show me the process to get the correct answer? The answer in the textbook is 4n.

Dick
Homework Helper
Since I'm having serious conceptual problems, can you show me the process to get the correct answer? The answer in the textbook is 4n.

m^4=(3^n)*(3^n)*(3^n)*(3^n)=3^(4n). What's log_3 of m^4? I don't know how else to explain this.

m^4=(3^n)*(3^n)*(3^n)*(3^n)=3^(4n). What's log_3 of m^4? I don't know how else to explain this.

Mkay, thank you for the aid, I'll see how it is tomorrow.

Dick