Help with "Rewrite the equation P = N*S^1/2 in logarithmic form."

[Ted_Grendy]

Hi all

I have a question about logs which I was trying to understand.

The question I have states Rewrite the following expression in log form:-

P = N*S^1/2

1) log P = log N*S^1/2
2) log P = log N + log S^1/2
3) log P = log N + 1/2* log S (I have taken the 1/2 exponent and dropped it to the log S as per the log laws).
4) log P = log N + log 1/2 + log S

I have been told the step 4 is incorrect and I cannot have log 1/2 but I am not sure why?

Can some one explain?

Thank you.

 

[Dr.Peterson]

The question I have states Rewrite the following expression in log form:-

P = N*S^1/2

1) log P = log N*S^1/2
2) log P = log N + log S^1/2
3) log P = log N + 1/2* log S (I have taken the 1/2 exponent and dropped it to the log S as per the log laws).
4) log P = log N + log 1/2 + log S

I have been told the step 4 is incorrect and I cannot have log 1/2 but I am not sure why?

The rule is that log(ab) = log(a) + log(b). If it had said log(1/2 S), you could transform it to log(1/2) + log(S). But the rule doesn't apply to 1/2 log(S), where the multiplication is outside the log.

That is, the log of a product is the sum of the logs; the expression there is not the log of a product, but a multiple of a log.

You were finished at step 3; the logs have been fully expanded, with nothing left to pull outside.

 

[Romsek]

Hi all

I have a question about logs which I was trying to understand.

The question I have states Rewrite the following expression in log form:-

P = N*S^1/2

1) log P = log N*S^1/2
2) log P = log N + log S^1/2
3) log P = log N + 1/2* log S (I have taken the 1/2 exponent and dropped it to the log S as per the log laws).
4) log P = log N + log 1/2 + log S

I have been told the step 4 is incorrect and I cannot have log 1/2 but I am not sure why?
.

\(\displaystyle \log\left(\dfrac 1 2 \log(S)\right) = \log\left(\dfrac 1 2\right) + \log(\log(S))\)

but that's not what's written in 3)

you have \(\displaystyle \dfrac 1 2 \log(S)\) NOT \(\displaystyle \log\left(\dfrac 1 2 \log(S)\right)\)

usually you'll just leave it as you've written in 3)

 

[Steven G]

Hi all

I have a question about logs which I was trying to understand.

The question I have states Rewrite the following expression in log form:-

P = N*S^1/2

1) log P = log N*S^1/2
2) log P = log N + log S^1/2
3) log P = log N + 1/2* log S (I have taken the 1/2 exponent and dropped it to the log S as per the log laws).
4) log P = log N + log 1/2 + log S

I have been told the step 4 is incorrect and I cannot have log 1/2 but I am not sure why?

Can some one explain?

Thank you.

We know that log S^(1/2) = 1/2* log S. Now if 1/2* log S = log 1/2 + log S, then log S^(1/2) = log 1/2 + log S. The problem is that this last equality is not true.

 

[Otis]

… log P = log N + 1/2* log S …
… log P = log N + log 1/2 + log S

I have been told the [last step above] is incorrect and I cannot have log 1/2 but I am not sure why? Can some one explain?

There's nothing wrong with the number log(1/2), so they shouldn't have said you can't "have" it. What they ought to have told you is that (1) you cannot take the logarithm of just a single term within an expression and (2) you did not apply the property correctly, anyways.

log(A∙B) = log(A) + log(B)

log(1/2∙log(S)) = log(1/2) + log(log(S))


Instead of beginning by taking the logarithm of each side, try isolating the power of S, first. (Divide each side by N.) Also, note that we need to type grouping symbols around exponents, when those exponents contain operation(s).

P/N = S^(1/2)

Now apply the property which allows us to switch back and forth between exponential notation and logarithmic notation:

A = b^n ⇔ n = log_b(A)

 

[Dr.Peterson]

Hi all

I have a question about logs which I was trying to understand.

The question I have states Rewrite the following expression in log form:-

P = N*S^1/2

1) log P = log N*S^1/2
2) log P = log N + log S^1/2
3) log P = log N + 1/2* log S (I have taken the 1/2 exponent and dropped it to the log S as per the log laws).
4) log P = log N + log 1/2 + log S

I have been told the step 4 is incorrect and I cannot have log 1/2 but I am not sure why?

Can some one explain?

Thank you.

Otis made an important point; what you are doing is taking the log of both sides and simplifying, but that is not what it says to do. What it says, taken literally, is that you are to write an equivalent equation using a log, which is what Otis did.

But then, I hope you didn't quote exactly what it said, because that is an equation, not an expression! The exact wording of a problem can be very important.

Most of us are probably assuming that you have seen other examples and know that this is what they intend for you to do; but you may be doing entirely the wrong thing.

Do you know what kind of answer is expected? Have you looked at the answers to this or other similar questions to verify that? This is part of the reason that books have answers in the back! Also, who told you that your answer is wrong? It is, as we've said (the log 1/2 should not be a separate term); but if it isn't your teacher, then they might also not be interpreting the question correctly.