The value of log₂(x/4) is 22. Using the properties of the logarithm, the required value is calculated.
<h3>What are the required properties of the logarithm?</h3>
The required logarithm properties are
logₐx = n ⇒ aⁿ = x; and logₐ(xⁿ) = n logₐ(x);
Where a is the base of the logarithm.
<h3>Calculation:</h3>
It is given that,
log₄(x) = 12;
On applying the property logₐx = n ⇒ aⁿ = x; here a = 4;
So,
log₄(x) = 12 ⇒ 4¹² = x
⇒ x = (2²)¹² = 2²⁴
Then, calculating log₂(x/4):
log₂(x/4) = log₂(2²⁴/4)
= log₂(2²⁴/2²)
= log₂(2²⁴ ⁻ ²)
= log₂(2²²)
On applying the property logₐ(xⁿ) = n logₐ(x);
log₂(x/4) = 22 log₂2
We know that logₐa = 1;
So,
log₂(x/4) = 22(1)
∴ log₂(x/4) = 22.
Learn more about the properties of logarithm here:
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Answer:
If the cap is left off, some of the dissolved CO2 can escape as gas from the bottle, making the pop go flat faster (less dissolved CO2 in pop). If the cap is placed tightly, the gaseous CO2 cannot readily escape the bottle thus your pop won't go flat
Explanation:
If the cap is left off, some of the dissolved CO2 can escape as gas from the bottle, making the pop go flat faster. If the cap is placed tightly, the gaseous CO2 cannot readily escape the bottle thus your pop won't go flat.
Just some fun related concept:
A similar concept comes into play for the reason behind why pop tastes better in fridge then just keeping at normal temperature. This is because gases tend to have high solubility at cold temperatures thus CO2 is more readily dissolved in fridge than outside room temperature which is why it tastes great!
The buoyancy of an object is dictated by its density. So let us calculate for density, where:density = mass / volume
Calculate the volume first of a solid cube:volume = (6 cm)^3 = 216 cm^3 = 216 mL
Therefore density is:density = 270 g / 216 mLdensity = 1.25 g / mL
Therefore this object will float in the layer in which the density is more than 1.25 g / mL.
You start by using proportions to find the number of liters of solution:
180 g of glucose / 1 liter of solution = 18 g of glucose / x liter of solution
=> x = 18 g of glucose * 1 liter of solution / 180 g of glucose = 0.1 liter of solution.
If you assume that the 18 grams of glucose does not apport volume to the solution but that the volume of the solution is the same volumen of water added (which is the best assumption you can do given that you do not know the how much the 18 g of glucose affect the volume of the solution) then you should add 0.1 liter of water.
Answer: 0.1 liter of water.
