Leo spent the same amount of time working on each of 5 different weight machines and then spent 2/3 of an hour on the treadmill. if he spent a total of 1 3/4 hours at the gym, which shows the correct equation and solution for x, the number of hours leo spent at each of the weight machines?

Let us say that the variable x is the amount of number of hours Leo spent at each of the weight machines.

Since there are 5 machines, therefore = 5 x

Adding this variable to the number of hours spent on the treadmill will give the total number of hours Leo spent at the gym. That is:

5 x + 2 / 3 = 1 3 / 4

5 x + 2 / 3 = 7 / 4

Therefore the correct equation is:

5 x + 2 / 3 = 7 / 4

Or if no denominator, we multiply the whole equation with 12 so that:

(5 x + 2 / 3 = 7 / 4) * 12

60 x + 8 = 21

or

60 x = 13

Solving for x will give:

x = 13 / 60

x = 0.217 hours

Leo spend 0.217 hours on each of the 5 machines.

you didn't post any answer choices, so its not 100% clear what your teacher is looking for

however, log(15/7) is equivalent to log(15) - log(7)

i'm using the rule log(x/y) = log(x) - log(y)