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Express the given expression as an integer or as a fraction in simplest form. (10^(log 10+log 7)) Answer:

Express the given expression as an integer or as a fraction in simplest form.\newline(10log⁡10+log⁡7) \left(10^{\log 10+\log 7}\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⁡10+log⁡7) \left(10^{\log 10+\log 7}\right) \newlineAnswer:
  1. Understand Properties of Logarithms: Understand the properties of logarithms.\newlineThe expression (10log⁡10+log⁡7)(10^{\log 10 + \log 7}) can be simplified using the properties of logarithms. Specifically, the property that states log⁡b(m)+log⁡b(n)=log⁡b(m∗n)\log_b(m) + \log_b(n) = \log_b(m*n) can be applied here.
  2. Apply Logarithm Property: Apply the logarithm property to combine the logarithms.\newlineUsing the property from Step 11, we can combine the logarithms inside the exponent:\newline10log⁡10+log⁡7=10log⁡(10×7)10^{\log 10 + \log 7} = 10^{\log(10\times7)}
  3. Simplify Expression Inside Logarithm: Simplify the expression inside the logarithm.\newlineNow we simplify the multiplication inside the logarithm:\newline10log⁡(10×7)=10log⁡(70)10^{\log(10\times7)} = 10^{\log(70)}
  4. Apply Definition of Logarithm: Apply the definition of a logarithm. The definition of a logarithm states that if bx=yb^x = y, then log⁡b(y)=x\log_b(y) = x. Applying this definition to our expression, we get: 10log⁡(70)=7010^{\log(70)} = 70

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