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Rewrite the square root as a fractional exponent.

Biology

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Answer

log⁡10y=12log⁡10x\log_{10} y = \frac{1}{2} \log_{10} x

Step-by-step solution

3 steps

  1. Rewrite the square root as a fractional exponent.

    y=x1/2y = x^{1/2}

  2. Take the logarithm base 10 (indicated by "LgK" and consistent with previous problems) of both sides of the equation.

    log⁡10y=log⁡10(x1/2)\log_{10} y = \log_{10} (x^{1/2})

  3. Apply the power rule of logarithms, log⁡b(Mc)=clog⁡bM\log_b (M^c) = c \log_b M.

    log⁡10y=12log⁡10x\log_{10} y = \frac{1}{2} \log_{10} x
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