Expand the logarithm into a sum or difference of logs with no exponents:

Question

Show step by step work:

log(16x³y⁵)

Answer 1

Logarithm Product Rule: The log of a product is equal to the sum of the logs of the factors:

log_b(m•n) = log_b(m) + log_b(n)

Logarithm Power Rule: The log of a number raised to an exponent is equal to the exponent multiplied by the log of the number:

log_b(mⁿ) = n•log_b(m)

SO:

Applying the Log Product Rule:

log(16x³y⁵) = log(16) + log(x³) + log(y⁵)

THEN:

Applying the log Power Rule:

log(16) + log(x³) + log(y⁵) = log(16) + 3log(x) + 5log(y)