Question about logarithms log math?

Question

Im totally lost with this...Im going to copy the question word by word... Please help...Correct answer gets 10 pts..

A black hole is a region in space where objects seem to disappear.A formula in the study of black holes is the Schwarzchild formula.

R= 2GM
-------------
c^2


Based on the laws of logarithms, log B can be represented by

A)2 logG + logM - log 2c

B)log 2G + log M- log 2c

C)log 2+ log G+ log M - 2 log c

D)2 log GM- 2 log c


If you may, can you explain how you got to the answer. Thanks I appreciate it much.

SORRY, GEEZA,,,,I meant to say

'Based on the laws of logarithms, log R can be represented by..'

Answer 1

The answer is C) log 2 + log G + log M - 2 log c

All I did was apply the three properties of logs:
for the numerator: log AB = log A + log B
for the denominator: log A/B = log A - log B
for the exponent: log A^p = p log A

that's it! :) (oh, I had to assume by B in your question you meant the R in the formula, right?)

Answer 2

So is the formula R = 2GM / (c^2)? And do you mean the log(R), not log(B)?

If that's the case, then you need to learn the rules of logs, which apply to logs of any base:

log(ab) = log(a) + log(b)
log(a/b) = log(a) - log(b)
log(a^b) = b log(a)

Apply the first two rules to split log(2GM / (c^2)) into four different log terms, then use the third rule to simplify the " - log(c^2)" at the end.

Answer 3

I don't know where logB would come from. The Schwarzchild formula calclates the radius of a black hole (the Schwarzchild radius, written r sub s. The formula is

r = 2 G m / c^2

where r is the radius, G is the gravitational constant, m is the mass and c is the speed of light.

log B is missing!

Answer 4

i will assume that in your question you meant to type log R not log B.

first take the log of both sides so log R = log(2GM/c^2)

and now apply the different rules for logs. there are the rules. i dont know the names:

log (a*b) = log a + log b
log (a/b) = log a - log b
log (a^b) = b*log a

hope this helps.
remember that these apply to any base logarithm.
read your math book!!!

Answer 5

Answer is (c)
log R = log 2 +log G + log M - 2 log C

Answer 6

)log 2+ log G+ log M - 2 log c

Answer 7

C is the correct answer.

The logarithm of a product is the sum of the logarithms; that's how you get the first three terms in C. When division is involved, you can subtract the logarithm; also when a power is involved you can multiply by the exponent. That's how the third term is developed.

Answer 8

Geezah is correct, they just didn't fully answer the question.
-log(c^2) = -2log(c) so the answer is C).

Answer 9

The answer is C.

I assume you mean log(R).
Use the rules of logs.

log(ab) = log(a) + log(b)
log(a/b) = log(a) - log(b)
log(a^b) = b log(a)

Now apply the rules to the problem.

R = 2GM/c²
log(R) = log(2GM/c²) = log(2GM) - log(c²)
= log(2) + log(G) + log(M) - 2log(c)

The answer is C.

Answer 10

Answer is C).

B=2*G*M/c^2
log(B)= log(2)+log(G)+log(m) - 2log(c)