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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The pressure of the gas used in the weather balloon increases to expand the balloon.
Explanation:
- Weather balloons contain the boxes where the weather measurement instruments are present that is attached to the large balloon.
- Weather balloon uses gases like Hydrogen or Helium. When the weather balloon rises to the atmosphere, the air pressure decreases. This leads to the increase in the pressure of hydrogen or Helium gas used in the weather balloon. This expands the balloon.
- The gas particles hits the balloon container and generates the pressure. The increase of pressure thus helps the weather balloon to move in a constant speed through the atmosphere.
A physical property of an element is a property of an element that can observed or measured without changing the chemical nature of the element.
A chemical property of an element is a property of an element that can only be observed or measure when the chemical property of the element is altered or changed.
Based on this;
The boiling point of bromine is a physical property of bromine.
The high reactivity of bromine with many elements is a chemical property of bromine.
Chemical change. Compounds and molecules in the milk are reacting with the air and breaking down and forming new molecules.
