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what is the value of xx when log⁡x+log⁡2=2\log x + \log 2 = 2?

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Full solution

Q. what is the value of xx when log⁡x+log⁡2=2\log x + \log 2 = 2?
  1. Combine logarithms: Combine the logarithms on the left side using the product rule for logarithms, which states that log⁡a+log⁡b=log⁡(ab)\log a + \log b = \log(ab).log⁡x+log⁡2=log⁡(2x)\log x + \log 2 = \log(2x)
  2. Set equal to 22: Set the combined logarithm equal to the right side of the equation.log⁡(2x)=2\log(2x) = 2
  3. Convert to exponential form: Convert the logarithmic equation to its exponential form. The base of the logarithm is 1010 by default when no base is specified, so the equation becomes 102=2x10^2 = 2x.\newline102=2x10^2 = 2x
  4. Calculate 10210^2: Calculate the value of 10210^2.\newline102=10010^2 = 100
  5. Set result equal: Set the result equal to 2x2x.\newline100=2x100 = 2x
  6. Divide by 22: Divide both sides of the equation by 22 to solve for xx.x=1002x = \frac{100}{2}
  7. Calculate xx: Calculate the value of xx.x=50x = 50

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