Question

Use the laws of logarithms to expand expression. log₁₀(x⁴y³z) 4 log(x) + 3 log(y) + log(z)

Answer 1

To expand the expression log₁₀(x⁴y³z), use the laws of logarithms to split it into separate terms and then combine like terms to simplify it.

Step-by-step explanation:

To expand the expression log₁₀(x⁴y³z),

1. Apply the rule of logarithm to separate the terms. We can write the expression as 4log₁₀(x) + 3log₁₀(y) + log₁₀(z).
2. Use the property that the logarithm of a product of two numbers is the sum of the logarithms of the two numbers. The expression can be further expanded as log₁₀(x) + log₁₀(x) + log₁₀(x) + log₁₀(x) + log₁₀(y) + log₁₀(y) + log₁₀(y) + log₁₀(z).
3. Combine like terms to simplify the expression. It becomes 4log₁₀(x) + 3log₁₀(y) + log₁₀(z).