SOLUTION: Determine logarithm of 59,436. My attempt: log 594 = 7738 (table). 4.7738 10^4.7738 = 59401. Where did I miscalculate? Non-homework.

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Determine logarithm of 59,436. My attempt: log 594 = 7738 (table). 4.7738 10^4.7738 = 59401. Where did I miscalculate? Non-homework.       Log On


   

Question 1147076: Determine logarithm of 59,436.
My attempt:
log 594 = 7738 (table).
4.7738
10^4.7738 = 59401.
Where did I miscalculate? Non-homework.



Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
59,436
5.9436%2A10%5E4
-
log%28%285.9436%2A10%5E4%29%29
log%28%285.9436%29%29%2Blog%28%2810%5E4%29%29
log%28%2810%5E4%29%29%2Blog%28%285.9436%29%29
4+0.7738, If use only the closest value in the table and not try to interpolate to look for a better value. You could try linear interpolation to get a better value.
( table found was http://www.sosmath.com/tables/logtable/logtable.html )

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


No miscalculation. If you use the table to find log(594) = 0.7738, then 10^4.7738 will be approximately 59400, which is what you found.

If you want a more accurate answer, you need to interpolate between the values given in the table.

Over very short intervals, the graph of a logarithm is nearly linear, so you can use linear interpolation.

log(594) = .7738
log(595) = .7745

The difference is .0007. Then a good approximation is

log(59436) = .7738 + .36(.0007) = .77405

Then using a calculator we find

10^4.77405 = 59436

to the nearest whole number -- which is what we want.