Use the Laws of Logarithms to expand the expression.
loga(x^5/yz^6)
and this was my answer and I got it wrong can any one tell me what I did wrong and what they got?
5log(x)-log(y)-6log(z)
That's right. Did it mark it wrong because you forgot to add the base? Or a different input format?
Four added to a number
To expand the expression loga(x^5/yz^6) using the Laws of Logarithms, we can follow these steps:
1. Start with the given expression: loga(x^5/yz^6).
2. Apply the quotient rule of logarithms, which states that loga(b/c) = loga(b) - loga(c). In this case, let's apply it to x^5 and yz^6 separately:
loga(x^5/yz^6) = loga(x^5) - loga(yz^6).
Since x is raised to the power of 5, we bring the exponent down as a coefficient:
= 5loga(x) - loga(yz^6).
3. Apply the product rule of logarithms, which states that loga(b * c) = loga(b) + loga(c). In this case, let's apply it to y and z^6 separately:
= 5loga(x) - (loga(y) + loga(z^6)).
Since z is raised to the power of 6, we bring the exponent down as a coefficient:
= 5loga(x) - loga(y) - 6loga(z).
Therefore, the correct expansion of loga(x^5/yz^6) is: 5loga(x) - loga(y) - 6loga(z). Your initial answer was correct; there might have been a mistake in the evaluation or marking process.
To expand the expression using the laws of logarithms, we can write it as:
loga(x^5/yz^6)
Using the quotient rule of logarithms, we can separate the numerator and denominator:
loga(x^5) - loga(y) - loga(z^6)
Next, using the power rule of logarithms, we can bring down the exponents as multipliers:
5loga(x) - loga(y) - 6loga(z)
So, the correct expansion of the given expression is:
5loga(x) - loga(y) - 6loga(z)
It seems like your answer is almost correct, but you made a mistake in the last term. Instead of writing -6log(z), it should be -6loga(z).