logarithms

Question

write 4log₁₁ 5-5log₁₁3 as a single logarithm

Answer 1

We will first use the logarithmic formula: n log_a b = log_a bⁿ, to bring the coefficients 4 and 5 as exponents

4log₁₁ 5 - 5log₁₁3 becomes

=log₁₁5⁴ - log₁₁3⁵

Since the base for both the log terms is the same (11), we can apply another logarithmic formula to combine the two logarithms terms into a single logarithm:

log_a x - log_a y = log_a (x/y)

= log₁₁ (5⁴/3⁵)

= log₁₁ (625/243)