Answer: x = -0.377
Step-by-step explanation:
We have the equation:
4^(5*x) = 3^(x - 2)
Now we can use the fact that:
Ln(A^x) = x*Ln(A)
Then we can apply Ln(.) to both sides of the equation to get:
Ln(4^(5*x)) = Ln(3^(x - 2))
(5*x)*Ln(4) = (x - 2)*Ln(3)
(5*x)*Ln(4) - x*Ln(3) = -2*Ln(3)
x*(5*Ln(4) - Ln(3)) = -2*Ln(3)
x = -2*Ln(3)/(5*Ln(4) - Ln(3)) = -0.377
There are 24 gallons of water that need to be split up into 3 buckets. How many gallons must each bucket hold? Y=number of gallons that each bucket holds.
Answer:
5.5 gallons
Step-by-step explanation:
set up a proportion; Liters in numerator and Gallons in denominator
let x = approx number of gallons
<u> 21 </u> = <u> 3.8 </u>
x 1
3.8x = 21
x = 21 ÷ 3.8
x ≈ 5.5
