What's the answer for this questionew with clear and explained working?

x = 5

Step-by-step explanation:

the whole equation is

2log(x) - 3log(2) + log(32) = 2

converting the first 2 expressions by using standard logarithm laws

2log(x) = log(x²)

3log(2) = log(2³) = log(8)

the combining these converted expressions again by using standard logarithm laws

log(x²) - log(8) = log(x²/8)

log(x²/8) + log(32) = log(32×x²/8) = log(4x²)

log(4x²) = 2

now dissolving the logarithm by converting every side to the power of 10.

4x² = 10² = 100

x² = 25

x = 5

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.