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Express the given expression as an integer or as a fraction in simplest form. (10^(log ((3)/(5)))) Answer:

Express the given expression as an integer or as a fraction in simplest form.\newline(10log⁡35) \left(10^{\log \frac{3}{5}}\right) \newlineAnswer:

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Full solution

Q. Express the given expression as an integer or as a fraction in simplest form.\newline(10log⁡35) \left(10^{\log \frac{3}{5}}\right) \newlineAnswer:
  1. Understand properties of logarithms: Understand the properties of logarithms and exponents.\newlineThe expression 10log⁡(35)10^{\log \left(\frac{3}{5}\right)} can be simplified using the property that alog⁡a(b)=ba^{\log_a(b)} = b, where aa is the base of the logarithm and the exponent. In this case, the base is 1010.
  2. Apply property to given expression: Apply the property to the given expression.\newlineSince the base of the logarithm and the exponent is the same 1010, we can simplify the expression directly to the argument of the logarithm, which is 35\frac{3}{5}.\newline10log⁡(35)=3510^{\log \left(\frac{3}{5}\right)} = \frac{3}{5}
  3. Check for simplest form: Check if the expression (35)(\frac{3}{5}) is already in its simplest form.\newlineThe fraction (35)(\frac{3}{5}) is already in its simplest form because 33 and 55 have no common factors other than 11.

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