Question

Evaluate log38, given log32 ≈ 0.631.

Answer 1

`\log_38-\log_32^3=3\log_32\approx3\cdot0.631=1.893\\\\Used:\log_ab^n=n\cdot\log_ab`

Answer 2

1.893

Explanation:

`log_3(8)`

first we write 8 in exponential form

8=2*2*2= 2*3

`log_3(2^3)`

Now we apply log property

`log_b(a^n)= n log_b(a)`

As per this property we move the exponent before log

`log_3(2^3)= 3 log_3(2)`

Given log_3(2) = 0.631

Plug in the value

`log_3(2^3)= 3 log_3(2)= 3*0.631= 1.893`