3 + 2 log (base 2) X = log (base 2) y

  • Thread starter Gughanath
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In summary, the equation "3 + 2 log (base 2) X = log (base 2) y" is used to find the value of X when given the value of y. The expression log (base 2) refers to the logarithm function with a base of 2. To solve for X, you can use algebraic manipulation to isolate the variable on one side of the equation. The equation represents a one-to-one relationship between X and y, and it can be solved using a calculator by using the "log" or "ln" function or by using the change of base formula.
  • #1
Gughanath
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3 + 2 log (base 2) X = log (base 2) y

how can this show, that y = 8X squared? Please help! :confused:
 
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  • #2
Rewrite this equality as follows:
[tex]2^{(3+2log_{2}x)}=2^{log_{2}y}[/tex]

Now, use properties of exponents and logarithms to derive the result!
 
  • #3
oh...I SEE...thanx...wasnt that hard :s
 
  • #4
how did u write the numbers (powers) above the normal number btw?
 
  • #5
Gughanath said:
how did u write the numbers (powers) above the normal number btw?
Click on the image to see the LATEX code behind it.
 

What is the equation "3 + 2 log (base 2) X = log (base 2) y" used for?

The equation "3 + 2 log (base 2) X = log (base 2) y" is used to find the value of X when given the value of y. It is often used in logarithmic calculations and in solving exponential equations.

What is the meaning of log (base 2) in this equation?

The expression log (base 2) refers to the logarithm function with a base of 2. This means that the value inside the parentheses is being raised to the power of 2.

How do you solve the equation "3 + 2 log (base 2) X = log (base 2) y" for X?

To solve for X, you can use algebraic manipulation to isolate the variable on one side of the equation. First, subtract 3 from both sides to get "2 log (base 2) X = log (base 2) y - 3". Then, use the power property of logarithms to rewrite the equation as "log (base 2) X^2 = log (base 2) (y - 3)". Finally, take the antilog of both sides to get X = √(y - 3).

What is the relationship between X and y in this equation?

The equation "3 + 2 log (base 2) X = log (base 2) y" represents a one-to-one relationship between X and y. This means that for every value of y, there is only one corresponding value of X that will satisfy the equation.

Can this equation be solved using a calculator?

Yes, this equation can be solved using a calculator. You can use the "log" or "ln" function on your calculator to find the logarithm of a number with a specific base. Some calculators also have a "log" button that automatically assumes the base to be 10, so you would need to use the change of base formula to get the correct answer.

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