Connections Academy help please?

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

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

Unit 7 Lesson 6!!

zehanz · Answer

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.

anonymous · Answer

Are you sure?

anonymous · Answer

@ZeHanz

zehanz · Answer

Yes, I'm sure!

zehanz · Answer

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!