How do you expand this log expression?
log(3x©÷¡îy/©ø¡î5z©÷)
To expand the given logarithmic expression, we need to apply the log properties. Here are the necessary steps:
Step 1: Break down the expression into separate logarithms using the properties of division and multiplication:
log(3x/5z) + log(sqrt(y))
Step 2: Apply the property of quotients to simplify the first logarithm. The property states that log(a/b) is equal to log(a) - log(b):
log(3x) - log(5z) + log(sqrt(y))
Step 3: Simplify further using the property of squares to eliminate the square root. The square root can be rewritten as raising the number to the power of 1/2:
log(3x) - log(5z) + log(y^(1/2))
Step 4: Use the property of exponents to bring the power of 1/2 inside the logarithm:
log(3x) - log(5z) + (1/2) * log(y)
So, the expanded form of the given logarithmic expression is:
log(3x) - log(5z) + (1/2) * log(y)