Question

Use the properties of logarithms to write as a single logarithm for the given equation: 1/2 log₂ x – 8 log₂ y – 5 log₂ z

Answer 1

By using the power rule , Log_b M^p = P log_b M, we can write the given equation as

1/2 log₂ x – 8 log₂ y – 5 log₂ z = log₂ x^1/2 – log₂ y⁸ – log₂ z⁵

From product rule, log_b MN = log_b M + log_b N

Take minus ‘- ‘ as common

1/2 log₂ x – 8 log₂ y – 5 log₂ z = log₂ x^1/2 – log₂ y⁸z⁵

From Quotient rule, log_b M/N = log_b M – log_b N

1/2 log₂ x – 8 log₂ y – 5 log₂ z = log₂ (x^1/2 / y⁸z⁵)