Find the exact value of the expression (with out a calculator): 81^(1/ln3)

Question

I mostly need help on what steps to take as I have to answer a lot of questions like this for an assignment.

Answer 1

Hi Sophia,

A = 81^(1/ln3)

1) take Ln of both side Ln A = Ln (81^(1/ln3) )

2) use property of power in log

Ln A = (1/ln3) * Ln (81 ) on the other hand 81 = 3^4 one more time use property

3) Ln A = (1/ln3) Ln (3⁴)

Ln A = (1/ln3) 4 Ln (3) now simplify Ln3

Ln A = 4 base of definition of log

A = e⁴

you can prof by using calculator and find e⁴ and given A, you will see both are 54.59815003

I hope it is useful,

Minoo