Solve for x by using log. rounded to hundredth.

Step-by-step explanation:

Given the expression , apply logarithm to both sides. Then:

Remembert that according the the properties of logarithms:

Then:

Appy distributive property and solve for "x":

x = 1.91

Step-by-step explanation:

* We have exponential equation to solve it lets study some rules

- If a^m = a^n ⇒ then m = n

- If a^m = b^m ⇒ then a = b or m = 0

- If a^m = b^n ⇒ log(a^m) = log(b^n) ⇒ m log(a) = n log(b)

* You can use log or ln

* Lets solve the problem

∵ ⇒ insert log to both sides

∴

-

∴ (2x - 5)log(4) = (-x + 1)log(6) ⇒ open the brackets

∴ 2xlog(4) - 5log(4) = -xlog(6) + log(6) ⇒ collect x in one side

∴ 2xlog(4) + xlog(6) = log(6) + 5log(4) ⇒ take x as a common factor

∴ x(2log(4) + log(6)) = log(6) + 5log(4)

- divide both sides by coefficient of x

∴ x = 1.91

d

step-by-step explanation:

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.