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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Water (H
2O) is a polar inorganic compound that is at room temperature a tasteless and odorless liquid, which is nearly colorless apart from an inherent hint of blue. It is by far the most studied chemical compound and is described as the "universal solvent" [18][19] and the "solvent of life".[20] It is the most abundant substance on Earth[21] and the only common substance to exist as a solid, liquid, and gas on Earth's surface.[22] It is also the third most abundant molecule in the universe.[21]
Water (H
2O)


NamesIUPAC name
water, oxidane
Other names
Hydrogen hydroxide (HH or HOH), hydrogen oxide, dihydrogen monoxide (DHMO) (systematic name[1]), hydrogen monoxide, dihydrogen oxide, hydric acid, hydrohydroxic acid, hydroxic acid, hydrol,[2] μ-oxido dihydrogen
Identifiers
CAS Number
7732-18-5 
3D model (JSmol)
Interactive image
Beilstein Reference
3587155ChEBI
CHEBI:15377 
ChEMBL
ChEMBL1098659 
ChemSpider
937 
Gmelin Reference
117
PubChem CID
962
RTECS numberZC0110000UNII
059QF0KO0R 
InChI
InChI=1S/H2O/h1H2 
Key: XLYOFNOQVPJJNP-UHFFFAOYSA-N 
SMILES
O
Properties
Chemical formula
H
2OMolar mass18.01528(33) g/molAppearanceWhite crystalline solid, almost colorless liquid with a hint of blue, colorless gas[3]OdorNoneDensityLiquid:[4]
0.9998396 g/mL at 0 °C
0.9970474 g/mL at 25 °C
0.961893 g/mL at 95 °C
Solid:[5]
0.9167 g/ml at 0 °CMelting point0.00 °C (32.00 °F; 273.15 K) [a]Boiling point99.98 °C (211.96 °F; 373.13 K) [6][a]SolubilityPoorly soluble in haloalkanes, aliphaticand aromatic hydrocarbons, ethers.[7]Improved solubility in carboxylates, alcohols, ketones, amines. Miscible with methanol, ethanol, propanol, isopropanol, acetone, glycerol, 1,4-dioxane, tetrahydrofuran, sulfolane, acetaldehyde, dimethylformamide, dimethoxyethane, dimethyl sulfoxide, acetonitrile. Partially miscible with Diethyl ether, Methyl Ethyl Ketone, Dichloromethane, Ethyl Acetate, Bromine.Vapor pressure3.1690 kilopascals or 0.031276 atm[8]Acidity (pKa)13.995[9][10][b]Basicity (pKb)13.995Conjugate acidHydroniumConjugate baseHydroxideThermal conductivity0.6065 W/(m·K)[13]
Refractive index (nD)
1.3330 (20 °C)[14]Viscosity0.890 cP[15]Structure
Crystal structure
Hexagonal
Point group
C2v
Molecular shape
Bent
Dipole moment
1.8546 D[16]Thermochemistry
Heat capacity (C)
75.375 ± 0.05 J/(mol·K)[17]
Std molar
entropy (So298)
69.95 ± 0.03 J/(mol·K)[17]
Std enthalpy of
formation (ΔfHo298)
−285.83 ± 0.04 kJ/mol[7][17]
Gibbs free energy (ΔfG˚)
−237.24 kJ/mol[7]
Answer:
1.07 g Ba
Explanation:
Hello there!
In this case, according to the definition of the Avogadro's number and the molar mass, it is possible to say that 6.022x10^{23} atoms of barium equal one mole, and at the same time, 1 mole equals 137.327 grams of this element; thus, it is possible to say that 6.022x10^{23} atoms of barium have a mass of 137.327 grams; therefore, it i possible for us to calculate the required mass in grams as shown below:

Best regards!
Answer:
2.57g
Explanation:
First, let us write a balanced equation for the reaction. This is illustrated below:
2H2 + O2 —> 2H2O
Next let us determine the limiting reactant. This is achieved as follows:
From the equation,
2L H2 required 1L of O2.
Therefore, 3.2L of H will require = 3.2/2 = 1.6L of O2
From the calculation above, O2 is excess because the volume of O2 given from the question is far greater than the volume of O2 obtained from our calculation. Therefore, H2 is the limiting reactant.
Now let us covert 3.2L of H2 to mole. This is illustrated below:
1mole of a gas occupy 22.4L at stp
Therefore, Xmol of H2 will occupy 3.2L i.e
Xmol of H2 = 3.2/22.4 = 0.143mol
From the equation,
2moles of H2 produced 2moles of H2O.
Therefore, 0.143mol of H2 will also produce 0.143moles of H2O.
Now, we can obtain the mass of the water vapour produced by convert 0.143mol of H2O to gram. This is illustrated below:
Molar Mass of H2O = (2x1) + 16 = 2 + 16 = 18g/mol
Number of mole of H2O = 0.143mol
Mass of H2O =?
Mass = mole x Molar Mass
Mass of H2O = 0.143 x 18 = 2.57g
The mass of water vapour produce is 2.57g