Final answer:
To find log5(xy⁴), we utilize logarithmic properties and the given values log5x = -4.6 and log5y = -11.9, resulting in log5(xy⁴) = log5x + 4 * log5y = -52.2.
Step-by-step explanation:
To find log5(xy⁴), we can use the property of logarithms that states the logarithm of a product is equal to the sum of the logarithms of the individual numbers. Additionally, the logarithm of a power is equal to the exponent times the logarithm of the base number.
Using the given values:
log5x = -4.6,
log5y = -11.9, and
log5r = -14.17,
we can set up the expression for log5(xy⁴) as follows:
log5(xy⁴) = log5x + 4 * log5y
Substituting the provided values, we get:
log5(xy⁴) = (-4.6) + 4 * (-11.9)
When we perform the multiplication and addition:
log5(xy⁴) = -4.6 + (-47.6) = -52.2