How to Find the Base in an Equations with Unknown Numbers

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In summary, a base in a scientific context is a substance that can accept protons or donate electrons in a chemical reaction, and has a pH level above 7. Bases can neutralize acids and increase pH levels, and some common examples include baking soda, ammonia, soap, and bleach. Bases have various everyday uses, such as in cleaning, cooking, and medicine, but they can also be corrosive to human skin and should be handled with caution.
  • #1
maxfails
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How would you solve a problem like this where you have to find what base A is for this equation to be true? So in what base are these numbers.24)A + 17)A = 40)A

Not asking the answer for this particular question but how you'd solve it (other than trial and error obviously)
 
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  • #2
A two digit number ab)A in base A equals [itex]A\cdot a + b[/itex] so:
24)A = 2A + 4
17)A = 1A + 7
40)A = 4A + 0
Then substitute in the equation and solve for A.
 
  • #3
Simple:

[tex]24_A = 2*A^1+4*A^0 = 2A + 4[/tex]

Similarly, [tex]17_A = 1A + 7[/tex] and [tex]40_A = 4A + 0[/tex]

Substitute and solve for A
 

1. What is a base in a scientific context?

A base in a scientific context refers to a substance that can accept protons (H+) or donate electrons in a chemical reaction. It is the opposite of an acid, and the two are often used together to neutralize each other.

2. How do bases affect pH levels?

Bases have a pH level above 7, which means they are alkaline. When bases are added to a solution, they can neutralize acids and increase the pH level, making the solution less acidic.

3. What are some examples of common bases?

Some examples of common bases include baking soda (sodium bicarbonate), ammonia, soap, and bleach. Many household cleaning products also contain bases.

4. How are bases used in everyday life?

Bases have a wide range of uses in everyday life, including cleaning, cooking, and medicine. For example, baking soda is used in baking and as a cleaning agent, and ammonia is used in household cleaners. Bases are also used in many industrial processes.

5. What happens when a strong base comes into contact with human skin?

Strong bases can be corrosive to human skin and can cause burns and irritation. It is important to handle strong bases with caution and wear protective gear, such as gloves and goggles, when handling them.

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