perplexus.info :: Just Math : Tiny Logs

Tiny Logs (Posted on 2025-05-08)

Given that log₁₀4=0.6021 to the nearest ten-thousandth, find log₁₀5 to the nearest thousandth.

No Solution Yet Submitted by Danish Ahmed Khan

No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)

Solution

Comment 1 of 1

log 10 = log(5*2) = log 5 + log 2 = 1 (these are base-10 logs)

log 4 = log(2^2) = 2 * log 2 = 0.6021 (given)

log 5 = 1 - log 2 = 1 - (log 4 / 2) = 1 - 0.6021 / 2 = 1 - 0.30105 = 0.69895

Rounded to the nearest thousandth, log 5 = 0.699

Posted by Paul on 2025-05-08 10:10:12

Please log in:

Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (4)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:


perplexus dot info