Question

Answer the following:

If a² = b³ = c⁴ = d⁵, show that log_a bcd = `47/30`

Answer 1

a² = b³ = c⁴ = d⁵

Taking log to the base a throughout, we get

log_a a² = log_a b³ = log_a c⁴ = log_a d⁵

∴ 2 log_a a = 3 log_a b = 4 log_a c = 5 log_a d

∴ 2(1) = 3 log_a b = 4 log_a c = 5 log_a d

∴ log_a b = `2/3`, log_a c = `2/4 = 1/2` and log_a d = `2/5`

∴ log_a b + log_a c + log_a d = `2/3 + 1/2 + 2/5`

∴ log_a bcd = `47/30`