Question

Use the properties of logarithms to write the expression as a single logarithm, if possible. 5 log₃ 4ω - 3 log₃ 5y + 2 log₃

O log₃ 1024ω⁵,x²/125y³
O log₃ 4ω⁵,x²/5y³
O log₃ (1024ω⁵ – 125y³ + x²)
O The expression cannot be written as a single logarithm
O log₃ 1024ω⁵/125y³ – x²
O log₃ 1024ω⁵/125y³x²

Answer 1

The expression 5 log₃ 4ω - 3 log₃ 5y + 2 log₃ 1024ω⁵ x²/125y³ can be rewritten as a single logarithm using logarithmic properties to yield log₃ (1024ωµ x²/125y³).

Step-by-step explanation:

To write the expression 5 log₃ 4ω - 3 log₃ 5y + 2 log₃ 1024ω⁵ x²/125y³ as a single logarithm, we apply the properties of logarithms:

• First, we use the property that log (a^b) = b log a, which allows us to bring the coefficients in front of the log terms up as exponents of their respective arguments inside the logs.
• Second, we use the property log ab = log a + log b and log (a/b) = log a - log b to combine the terms into a single logarithm.

This gives us:

log₃ ((4ω)^5 / (5y)^3 × 1024ω⁵ x²/125y³)
After simplifying the expression within the logarithm and reducing where possible, we obtain:

log₃ (1024ωµ x²/125y³)

This is equivalent to the original expression rewritten as a single logarithm.