Question

What is the value of log subscript a open parentheses fraction numerator x y cubed over denominator z to the power of short dash 2 end exponent end fraction close parentheses when given the following values? log subscript a open parentheses x close parentheses equals 4 log subscript a open parentheses y close parentheses equals 2 log subscript a open parentheses z close parentheses equals short dash 6

Answer 1

To find the value of log_subscript a(x^3y/z^-2) using the given values of log_subscript a(x), log_subscript a(y), and log_subscript a(z), substitute the values into the expression and simplify using the properties of logarithms.

Step-by-step explanation:

Given the values of loga(x), loga(y), and loga(z), we can substitute these values into the given expression for loga(x3y/z-2). Applying the properties of logarithms, we can simplify the expression as follows:

1. Substitute the values of loga(x), loga(y), loga(z) into the given expression.
2. Simplify by applying the property loga(M/N) = loga(M) - loga(N).
3. Evaluate each logarithm using the given values.
4. Substitute the resulting values into the simplified expression.

By following these steps, you can find the value of loga(x3y/z-2) using the provided values.