Log of 27 times 4th-rt of 9 times 3rd-rt of 9 to base 3 is ?

[natalie462]

**I know how to solve this on a calculator but have no idea how to use it without one**

The logarithm of 27 times the fourth root of 9 times the third root of 9 to the base of 3 is ____________.

 

[Mrspi]

Re: Logarithm Problem

**I know how to solve this on a calculator but have no idea how to use it without one**

The logarithm of 27 times the fourth root of 9 times the third root of 9 to the base of 3 is ____________.

If I understand you problem, you are looking for the log (base 3) of this expression:

27 * 9^(1/4)*9^(1/3)

I guess I'd try to express each of these factors as a power of 3.....

27 is 3^3

9^(1/4) is the same thing as (3^2)^(1/4), or 3^(1/2)

9^(1/3) is the same thing as (3^2)^(1/3), or 3^(2/3)

So....

27 * 9^(1/4) * 9^(1/3)

can be written as

3^3 * 3^(1/2) * 3^(2/3)

You're multiplying powers of the same base. The rule for exponents says to ADD the exponents when you multiply.

3^3 * 3^(1/2) * 3^(2/3) = 3^[3 + (1/2) + (2/3)]


finally...log(base 3) 3^n = n

I've done most of the work for you...if you're still having trouble with this problem, please repost showing ALL of the work you have done to try to finish the problem.