If log a^2 is about .36 , log a^3 is about .56 and log a ^5 is about .83 then what is log a^8?

Answer 1

Actually, you only need one of those to find log(a^8).

I'll use log(a^2):
log(a^2) = 0.36
10^0.36 = a^2
a = ±1.51

log(1.51^8)
= log(27.03)
= ln(27.03) / ln(10)
= 3.3 / 2.303
= 1.43

Answer 2

a^8 = [(a^5)(a^2)/(a^3)]^2

log a^8 = 2 [ log a^5 + log a^2 - log a^3]
= 2 [ .83 + .36 - .56 ]
= 2 (.63) = 1.26

Answer 3

I'm sure they want you to use your rules of logarithms you've learned to break down a^8 into parts so you can use the given three statements. Some possiblities (which will all give you the same answer):

a^8 = (a^2)^4

a^8 = a^5 * a^3

a^8 = a^3 * a^3 * a^2

etc.

Now break the right hand side of one of those apart using the rules you've learned, and then substitute the values given to find the final answer.

Answer 4

log a^8 = 4log a^2 = 4(.36) = 1.44

Answer 5

log a^8 is about 8*.18 = 1.44