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Given that log a = 0.30 and log b = 0.48, find the value of log (b2 / a).

Mathematics

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Answer

0.66

Step-by-step solution

4 steps

Here's how to find the value of log⁡b2a\log \frac{b^2}{a}:

  1. Apply the logarithm property for division, log⁡(MN)=log⁡M−log⁡N\log \left(\frac{M}{N}\right) = \log M - \log N.

    log⁡b2a=log⁡(b2)−log⁡a\log \frac{b^2}{a} = \log (b^2) - \log a

  2. Apply the logarithm property for powers, log⁡(Mk)=klog⁡M\log (M^k) = k \log M.

    log⁡(b2)−log⁡a=2log⁡b−log⁡a\log (b^2) - \log a = 2 \log b - \log a

  3. Substitute the given values, log⁡a=0.30\log a = 0.30 and log⁡b=0.48\log b = 0.48.

    2(0.48)−0.302(0.48) - 0.30

  4. Perform the multiplication and subtraction.

    0.96−0.30=0.660.96 - 0.30 = 0.66
    • 0.66
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