SOLUTION: Write the equation in logarithmic form n^(4/3)=m Please help!

Algebra ->  Test  -> Lessons -> SOLUTION: Write the equation in logarithmic form n^(4/3)=m Please help!       Log On


   

Question 695601: Write the equation in logarithmic form
n^(4/3)=m
Please help!
Found 2 solutions by KMST, RedemptiveMath:
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
What's expected is probably highlight%28log%28n%2Cm%29=4%2F3%29
That comes straight out of the definition of logarithm.

Or maybe you were expected to use the common, base 10 logarithms and take logarithms of both sides, like this:
n%5E%284%2F3%29=m --> log%28%28n%5E%284%2F3%29%29%29=log%28%28m%29%29 --> highlight%28%284%2F3%29log%28%28n%29%29=log%28%28m%29%29%29 <--> highlight%28log%28%28n%29%29=%283%2F4%29log%28%28m%29%29%29

Answer by RedemptiveMath(80) About Me  (Show Source):
You can put this solution on YOUR website!
The logarithm is like a unique way of writing exponential functions. A general exponential function is given in the form y = b^x, where b is called the base, x is called the exponent and y can be called the product of factors. A logarithmic function, however, is given the form logb (y) = x. (The b is written as a subscript. That is, it should be written to the bottom and right of "log" and in tinier font.) If you look at these two forms, you may notice something:

y = b^x and logb (y) = x.

The b is with the x in the first form, but the b is with the y in the second form. Logarithms are another way of writing exponential functions. This form however lets us know what the exponent x is from the logarithm base b of the product of factors y. Let us use an example to illustrate these two forms.

4^2 = 16

This is exponential form. The base is 4, the exponent is 2, and the solution is 16. Let's look at these numbers written in logarithmic form:

log4 (16) = 2.

If we write both forms in the same direction (the answer on the right), we can see that the base 4 doesn't switch sides. It is still on the left side. The two things that switch are 16 and 2. The first form we are worried about finding the product of factors, which is 4 * 4 or 16. The second form we are worried about finding the exponent from a base and a product of factors. Of course we could be worried about finding any of the three parts if we use variables, but the general notion is as described. Let us now look at our problem:

n^(4/3)=m.

We can see that this is written in exponential form y = b^x. The base in the problem is n, the exponent is 4/3 and the product of factors or solution is m. Applying the rules for logarithmic functions above, let us convert into that form:

n^(4/3)=m
logn (m) = 4/3.

Remember that n must be in subscript form. This is read as "log base n of m equals 4/3."