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Answer

2.089

Step-by-step solution

3 steps

Here's how to solve the problem:

  1. Understand the definition of logarithm.

    The equation log⁡α=0.32\log \alpha = 0.32 implies a base-10 logarithm, meaning log⁡10α=0.32\log_{10} \alpha = 0.32.
    To convert a logarithmic equation to an exponential equation, we use the definition: if log⁡bx=y\log_b x = y, then by=xb^y = x.

  2. Convert to exponential form.

    Using the definition, with b=10b=10, x=αx=\alpha, and y=0.32y=0.32:

    α=100.32\alpha = 10^{0.32}
  3. Calculate the value of α\alpha.

    Using a calculator to evaluate 100.3210^{0.32}:

    α≈2.089296\alpha \approx 2.089296

    Rounding to a reasonable number of decimal places (e.g., three decimal places):

    α≈2.089\alpha \approx 2.089

    The value of α\alpha is 2.089\boxed{2.089}.

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