Use the Laws of Logarithms to expand the expression.
loga(x^5/yz^6)
Can anybody help me step by step pleassse?
log(a^b) = b*log(a)
log(u/v) = log(u)-log(v)
So, you have
5log(x)-log(y)-6log(z)
where all the logs are base a.
Sure! I'd be happy to help you step by step.
To expand the expression using the Laws of Logarithms, we can use a combination of the Product Rule and the Quotient Rule.
First, let's start with the provided expression:
loga(x^5/yz^6)
According to the Quotient Rule, we can separate the numerator and denominator into two separate logarithms with subtraction:
loga(x^5) - loga(yz^6)
Now, let's simplify each logarithm individually.
For the first logarithm, loga(x^5), we can use the Power Rule to bring the exponent down in front:
5loga(x)
For the second logarithm, loga(yz^6), we can use the Product Rule to separate the variables:
loga(y) + loga(z^6)
Now, let's substitute these simplified logarithms back into the original expression:
5loga(x) - (loga(y) + loga(z^6))
Since we have a negative sign before the parentheses, we need to distribute the negative sign to each term inside the parentheses:
5loga(x) - loga(y) - loga(z^6)
And there you have it! The expanded expression using the Laws of Logarithms is:
5loga(x) - loga(y) - loga(z^6)