Expand each logarithm.
log 7(3x-2)^2
log(3xyz)^2
Thanks in advance.
One.
log7(3x-2)^2= log7 + 2 log (3x-2)
To expand the logarithm log7(3x-2)^2, you can use the property log(a^n) = n log(a). Here's how to do it step by step:
1. Start with log7(3x-2)^2.
2. Apply the property log(a^n) = n log(a) to the quantity (3x-2)^2: log7((3x-2)^2) = 2 log7(3x-2).
3. Now, you can rewrite the expression as log7 + 2 log (3x-2). The reason for this is that log7 is always a constant and can be separated from the logarithm of the expression inside parentheses.
So, the expanded form of log7(3x-2)^2 is log7 + 2 log (3x-2).
Two.
For log(3xyz)^2, you can use the property log(a^n) = n log(a) to expand the logarithm. Here's how to do it step by step:
1. Start with log(3xyz)^2.
2. Apply the property log(a^n) = n log(a) to the quantity (3xyz)^2: log((3xyz)^2) = 2 log(3xyz).
3. Since the logarithm is applied to the entire expression 3xyz, you don't need parentheses around it.
4. Now, the expression is expanded to 2 log(3xyz).
So, the expanded form of log(3xyz)^2 is 2 log(3xyz).