Answer:
4^((3x+4)/4).
Explanation:
The expression log4(3x+4)-2 represents the logarithm of the quantity (3x+4) to the base 4, minus 2.
To simplify this expression, let's break it down step by step:
Step 1: Apply the logarithmic property of subtraction. According to this property, loga(b) - loga(c) = loga(b/c).
So, log4(3x+4)-2 can be written as log4(3x+4)/4.
Step 2: Evaluate the logarithm. Remember that loga(b) is the exponent to which a must be raised to obtain b.
In this case, we have log4(3x+4)/4. This means 4 raised to the power of what equals (3x+4)/4.
Step 3: Simplify further. Since we're dealing with logarithms to the base 4, we need to find the exponent to which 4 must be raised to obtain (3x+4)/4.
This can be written as 4^((3x+4)/4).
Step 4: Simplify the exponent. Since the exponent (3x+4)/4 is already in its simplest form, we don't need to further simplify it.
Therefore, the final simplified expression is 4^((3x+4)/4).
I hope this helps!