Comparing Powers of Different Bases How can I know if one power is bigger than the other when th

Aaden Lam

Aaden Lam

Answered question

2022-01-22

Comparing Powers of Different Bases
How can I know if one power is bigger than the other when the bases are different?
For example, considering 210 and 103 the former is the greater one, but how to prove this? Logarithms? I'll be working with big numbers, and though a more general solution is really appreciated, I will be comparing exactly powers of 2 and 10.

Answer & Explanation

Tyrn7i

Tyrn7i

Beginner2022-01-23Added 11 answers

log2 is the way to go.
log2(22000)=2000
log2(10800)=800log2(10)
So which is bigger 20 or 8log2(10)?
Let's see 20 is smaller than 8×3=24 and
log2(10)>log2(8)=log2(23)=3. So it looks like:
22000<10800
(no calculator required).
To compare:
3=log2(23)=log2(8)<log2(10)<log2(16)=log2(24)=4

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?