Why ( 2 + Log5÷log2) Different from ( Log5÷log2 + 2)

  • Thread starter r-soy
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In summary, the values of ( 2 + Log5÷log2) and ( Log5÷log2 + 2) are different due to the order of operations not being followed in the same way. The logarithms in both expressions manipulate the numerical values in a specific way, resulting in different overall values. These expressions can be simplified using the properties of logarithms. They have real-life applications in various fields such as mathematics, engineering, and science. Logarithms are used in these expressions to simplify complex calculations, compare values, and have many applications in science and engineering.
  • #1
r-soy
172
1
Hi

why ( 2 + Log5÷log2) Different from ( Log5÷log2 + 2)

please i want help
 
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  • #2
From exactly how you have written it, it isn't. Are there any other brackets you may have omitted?
 
  • #3
r-soy said:
Hi

why ( 2 + Log5÷log2) Different from ( Log5÷log2 + 2)

please i want help
What you have written: [itex]2+ \frac{log 5}{log 2}[/itex] is not at all different from [itex]\frac{log 5}{log 2}+ 2[/itex].

If you mean [itex]\frac{2+ log 5}{log 2}[/itex] then that is quite different. It is just that the way you are writing it is not clear whether you mean 2+ (log 5/log 2) or (2+ log 5)/log 2.
 

1. Why are the values of ( 2 + Log5÷log2) and ( Log5÷log2 + 2) different?

The values of ( 2 + Log5÷log2) and ( Log5÷log2 + 2) are different because the order of operations, also known as the "PEMDAS" rule, is not followed in the same way. In the first expression, the addition occurs before the division, while in the second expression, the division occurs before the addition. This leads to different results.

2. How do the logarithms in ( 2 + Log5÷log2) and ( Log5÷log2 + 2) affect the overall value?

The logarithms in both expressions affect the overall value by manipulating the numerical values in a specific way. In the first expression, the logarithm of 5 is divided by the logarithm of 2, which results in a smaller value. In the second expression, the logarithm of 2 is divided by the logarithm of 5, which results in a larger value. These values are then added to 2, leading to different final results.

3. Can the expressions ( 2 + Log5÷log2) and ( Log5÷log2 + 2) be simplified?

Yes, these expressions can be simplified by using the properties of logarithms. For example, the expression ( 2 + Log5÷log2) can be rewritten as (Log5/log2 + 1 + 1), which can then be further simplified to (Log5/log2 + 2). Similarly, the expression ( Log5÷log2 + 2) can be rewritten as (Log5/log2 + 1 + 1), which can then be simplified to (Log5/log2 + 2).

4. Are there any real-life applications for these expressions?

Yes, these types of expressions are commonly used in various fields such as mathematics, engineering, and science. For example, in chemistry, the pH scale is calculated using logarithms. In physics, the decibel scale for sound intensity also uses logarithms. These expressions are also useful in data analysis and modeling.

5. Is there a specific reason for using logarithms in these expressions?

Yes, logarithms are used in these expressions because they can help simplify complex mathematical calculations. They are also useful for comparing values that vary by a large range. In addition, logarithms have many applications in science and engineering, making them a valuable tool for solving problems and analyzing data.

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