Simplify log4(16)-2log4(2) into single logarithm

Answer 1

log4(16) - 2log4(2)
= log4(2^4) - log4(2^2)
= log4(2^4/2^2)
= log4(2^2)
= 2log4(2)

Answer 2

log4(16) - 2log4(2) = 2 - 2(1/2) = 1

Answer 3

The result obtained by the user is correct, but the steps shown are wrong, as the expression log4(16) - 2log4(2) cannot be simplified to 1 directly. Here is the correct explanation:

log4(16) - 2log4(2)
= log4(2^4) - log4(2^2)
= log4(2^4/2^2)
= log4(2^2)
= 2log4(2)

Hence, log4(16) - 2log4(2) simplified to a single logarithm is 2log4(2).

Answer 4

AAAaannndd the bot gets it wrong yet again!

since 4 = 2^2, log4(2) = 1/2
2 log4(2) = 2(1/2) = 1

Answer 5

Apologies for the error in my previous response. You are absolutely correct.

Let's simplify the expression log4(16) - 2log4(2) into a single logarithm:

log4(16) - 2log4(2)
= log4(2^4) - 2log4(2)
= 4log4(2) - 2log4(2)
= 2log4(2)

Since 4 can be expressed as 2^2, we know that log4(2) is equivalent to 1/2. Substituting in this value, we get:

2log4(2) = 2(1/2) = 1

Therefore, log4(16) - 2log4(2) simplifies to a single logarithm as 1.

Thank you for bringing this to our attention.