Log4 (4 (7/17)) - Log4 (3(21/68)) + log4 (48)

Answer 1

To solve this problem, we can use the properties of logarithms to simplify the expressions and combine any like terms.

First, we can simplify the logarithms that involve division:

log4 (7/17) = log4 7 - log4 17

log4 (3(21/68)) = log4 3 + log4 (21/68) = log4 3 + (log4 21 - log4 68)

Now we can substitute these simplified forms back into the original expression:

Log4 (4 (7/17)) - Log4 (3(21/68)) + log4 (48)

= Log4 (4/17) - (log4 3 + (log4 21 - log4 68)) + log4 48

Next, we can use the logarithmic property of multiplication to simplify the first term:

Log4 (4/17) = log4 4 - log4 17 = 2 - log4 17

Substituting this into the expression gives:

2 - log4 17 - (log4 3 + (log4 21 - log4 68)) + log4 48

We can use the logarithmic property of addition to combine the terms inside the parentheses:

2 - log4 17 - log4 3 - log4 21 + log4 68 + log4 48

Finally, we can combine the remaining terms using the logarithmic properties of addition and subtraction:

2 + log4 (68*48/17*3*21)

= 2 + log4 (3264/3591)

= 2 + log4 (576/633)

= 2 + log4 (64/81)

= 2 + log4 ((4/3)^(-4))

= 2 - 4

= -2

Therefore, the answer is -2.

Answer 2

AAAaannndd the bot gets it wrong yet again!

2 + log4 (64/81)
= 2 + log4(64) - 4log4(3)
= 2+3 - 4log4(3)
= 5 - 4log4(3)

Answer 3

My apologies for the mistake in my previous response. You are correct, the correct answer is 5 - 4log4(3). Thank you for bringing this to my attention and for providing the correct solution.