Question

Evaluate: Log_{5} 16 / Log_{5} 4 (no calculator)

Answer 1

\[2^{-x} = 8\] find exact solution, use common log and two decimal place approximation of each

Answer 2

x=(-3)\[2^{-(-3)}=2^{3}=8\]

Answer 3

Either I worked it wrong, but that one can be solved by inspection. Now I will think about solving it with logs.

Answer 4

Yes, please. It is in my precalculs book and they are using logs in this chapter. Thank you.

Answer 5

I am very rusty with logs lol. But here is my go at it.
-x log2 = log 8
-0.301029x=0.90308998
x=-0.90308998/0.301029=-3.000009923 for 2 decimal place approximation
x=-3.00

Answer 6

Looks like it still is a -3

Answer 7

Thank you!