Question

Logbase3 logbase2 logbase root 3 81=1

Answer 1

Answer:

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Answer 2

Answer:

1

Step-by-step explanation:

Given--->

log₃ { log₂ (log 81) }

√3

To find ---> Value of given expression

Solution--->

We have some formulee of log

1) log xⁿ = n logx

2) log ₙ n = 1

3) log ₙ m = logm / logn

Applying these formulee first we solve

log 81 = log 81 / log √3

√3

= log 3⁴ / log (3)¹/²

= 4 log 3 / (1/2) log 3

log 3 cancel out from numerator and denominator

= 4 × 2

= 8

Now concentrating on original problem

log { log (log 81 ) }

3 2 √3

= log { log ( 8 ) }

3 2

= log { log ( 2 × 2 × 2 ) }

3 2

= log { log ( 2³ ) }

3 2

= log ( 3 log 2 )

3 2

= log ( 3 × 1)

3

= log 3

3

= 1