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Solve for a positive value of x. log_(2)(x)=7 Answer:

Solve for a positive value of x x .\newlinelog⁡2(x)=7 \log _{2}(x)=7 \newlineAnswer:

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Full solution

Q. Solve for a positive value of x x .\newlinelog⁡2(x)=7 \log _{2}(x)=7 \newlineAnswer:
  1. Identify Property of Logarithms: Identify the property of logarithms to solve for xx. The equation log⁡2x=7\log_{2}x = 7 can be rewritten using the definition of a logarithm, which states that if log⁡ba=c\log_{b}a = c, then bc=ab^{c} = a.
  2. Convert to Exponential Form: Convert the logarithmic equation to its exponential form.\newlineUsing the property from Step 11, we can write the equation as 27=x2^7 = x.
  3. Calculate Exponential Value: Calculate the value of 22 raised to the power of 77. \newline27=1282^7 = 128
  4. Verify Positive Solution: Verify that the solution is a positive value.\newlineSince 128128 is a positive number, we have found the positive value of xx that satisfies the equation.

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