Question

Evaluate the log


`Log_(3)81`=

Answer 1

Solve \bf{log_3 \:81}log

3

81

Answer :

\bf{log_3 \:81=4}log

3

81=4

Factor the number 81 :

Prime factorization: 81 = 3 × 3 × 3 × 3

= 3⁴

So, \bf{log_3 \:81} = log _3\left(3^4\right)}

Apply Log Rule : \bf{log _a\left(a^x\right)=x}log

a

(a

x

)=x

\bf{log _3\left(3^4\right)} = 4log

3

(3

4

)=4

Answer 2

9514 1404 393

Answer:

log₃(81) = 4

Explanation:

There are a few ways you can go at this. Perhaps the simplest is to recognize that 81 is a power of 3.

log₃(81) = log₃(3⁴)

log₃(81) = 4

__

You can also use the "change of base" formula:

log₃(81) = log(81)/log(3) ≈ 1.908485/0.4771213

log₃(81) = 4

__

A suitable calculator works, too.