Can anyone help me solve this math problem?

Question

Write the log as a single quantity.

1/2 [4 log (x - 2) + log (x + 3 ) - log 5]

Answer 1

First 4*log[x-2] = log[x-2]^4.
Then -log[5] = log[1/5]

The sum of logs is the log of the product of the arguments and so this gives

(1/2)*log[(x-2)^4 * (x+3) / 5]

Finally the (1/2) becomes an exponent in the argument:

log[((x-2)^4 * (x+3) / 5)^(1/2)]

Answer 2

=1/2[log(x-2)^4+log(x+3)-log5]
=1/2[log((x-2)^4x(x+3))/5]
=log[((x-2)^4.(x+3)/5)^(1/2)]