Question

Connections Academy help please?

2. Use the Change of Base Formula to evaluate log[8]77.
3.467
1.886
4.344
2.089

Answer 1

\[\log_8(77)=\frac{\ln(77)}{\ln(8)}\] and a calculator

Answer 2

I don't have my calculator. Can you tell me the answer?

Answer 3

Unit 7 Lesson 6!!

Answer 4

Because you do not really have to calculate anything, you can make an educated guess: \[\log_{8}77=a <=> 8^a=77 \]
Now 8^2 =64, so 8^2.... = 77, because 77 is only slightly larger than 64.
The only answer that fits is therefore 2.089.

Answer 5

Are you sure?

Answer 6

@ZeHanz

Answer 7

Yes, I'm sure!

Answer 8

8 = 8^1, so log(8)8=1
64=8^2, so log(8)64=2
512=8^3, so log(8)512=3

See? That's why log(8)77 must be only a little more than 2!