Use the Laws of Logarithms to combine the expression.?

Question

log12 + 1/2log7 - log2

Answer 1

OK, you really need to try to do a few of these on your own.
I'm going to give you a hint:

Use the law that says
log(x) + log(y) = log(x*y)

and log(x) - log(7) = log(x/y)

Answer 2

First, take a look at the 1/2 (in 1/2 log 7). If you have a coefficient in front of the logarithm, you can take the number inside the logarithm (in this case, the 7) and raise it to the power of the coefficient. So, the steps would look like this:

1/2 log 7 = log 7^(1/2) = log (sqrt(7))

The rest of it is simply done left to right. Since all these logs are base 10, you can combine all the numbers inside the logs that are ADDED by multiplying. If the log is SUBTRACTED, you divide.

So, we have:

log 12 + log sqrt(7) - log 2

We multiply the first two numbers inside the log, since they are added:

log (12*sqrt(7)) - log 2

Then simply divide the number inside the log by 2 to get:

log (6*sqrt(7)).

I hope this helps you out.

Answer 3

Ok

log (Q*M) = log Q +log M

log (1/Q) = -log(Q)

log (Q^R)= R log (Q)

So:
log (12) + (1/2)log (7) -log (2)
log (12) + log(7^(1/2)) +log (1/2)

combining the first and third logarithms:

log (6) +log(7^(1/2)) , combine these:
log {(6)(7^(1/2))}

Answer 4

log(12) + (1/2)log(7) - log(2)
log(12) + log(7^(1/2)) - log(2)
log((12 * 7^(1/2))/2)
log(6 * 7^(1/2))