Problem

Express as a difference of logarithms. Assume $\mathrm{z}$ is a positive real number. \[ \log \frac{10}{z} \] \[ \log \frac{10}{z}=\square \] (Type an exact answer in simplified form.)

Solution

Step 1 :Express the given expression as a difference of logarithms. Assume z is a positive real number: \(\log \frac{10}{z}\).

Step 2 :According to the properties of logarithms, the logarithm of a quotient is equal to the difference of the logarithms of the numerator and the denominator.

Step 3 :Therefore, we can express the given expression as the difference of the logarithm of 10 and the logarithm of z: \(\log 10 - \log z\).

Step 4 :Final Answer: \(\boxed{\log 10 - \log z}\)

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