Solve Logarithm Problem: "log3m4, in terms of n

[Aokei]

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 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)?

 

[Aokei]

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]

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?

 

[Aokei]

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]

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?

 

[Aokei]

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]

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.

 

[Aokei]

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]

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.

 

[Aokei]

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]

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

Sure, just think it over. It's not that strange.