Logarithm help?

If the question is stated accurately, it takes 5 hours. But that is too easy.

I think it's supposed to be 10% of the distance in the first hour,

10% of the remaining distance in the second hour,

10% of the remaining distance in the third hour,

etc.

x = starting distance

0.10x traveled in the first hour; 0.90x distance remains.

0.10(0.90x) traveled in the second hour; 0.90(0.90x) distance remains.

0.10(0.90²x) traveled in the third hour; 0.90(0.90²x) distance remains.

etc.

After n hours, 0.90³x distance remains.

0.90ⁿx = 0.5x

0.90ⁿ = 0.5

take log base 0.90 of both sides

n = 6.578813479

It takes about 6.6 hours to travel halfway.

I don't see the use of logarithms into this.It seems a simple problem,

If 10 % of his/her journey is completed in 1 hour than remaining 90 % will be completed in 9 hrs.So,the total time required to complete journey will be 9+1 =10 hrs.

So ,half of the journey will be done in 10/2=5 hrs.

if a person moves 10% of the distance in one hour, then 90% remains...

(0.90)^n = (0.50)

n log (0.90) = log (0.50)

n = [log (0.50)]/[log (0.90)] ≈ 6.5788 hours

check...do something