Question

Розв'язати log5(log4(log3(81)))

Answer 1

по определению логарифма:

log3(81) = 4 ( 3⁴ = 81 )

log4(log3(81)) = log4(4) = 1 ( 4¹ = 4 )

log5(1) = 0 ( 5⁰ = 1 )

Answer 2

To solve the expression log₅(log₄(log₃(81))), we'll work from the inside out.

Step 1: Calculate log₃(81) log₃(81) = ? (Find the exponent to which 3 must be raised to get 81)

3^4 = 81 So, log₃(81) = 4

Step 2: Calculate log₄(log₃(81)) log₄(log₃(81)) = ? (Find the exponent to which 4 must be raised to get the result of step 1)

4^4 = 256 So, log₄(log₃(81)) = 4

Step 3: Calculate log₅(log₄(log₃(81))) log₅(log₄(log₃(81))) = ? (Find the exponent to which 5 must be raised to get the result of step 2)

5^4 = 625 So, log₅(log₄(log₃(81))) = 4

The final result is 4.