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Given log a = b, express 10^(2b-3) in terms of a.

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Final answer:

The expression 10^(2b-3) given that log a = b can be rewritten as a^2/1000 by using properties of logarithms and exponents.

Step-by-step explanation:

According to the given, log a = b. This equation in another form is a = 10^b. When we have 10^(2b-3), we can split that exponent to rewrite the expression like this: 10^(2b) * 10^(-3).

According to the laws of exponentiation, 10^(2b) can be re-written as (10^b)^2, which we already know can be expressed as a^2 (since 10^b = a). So 10^(2b-3) can be rewritten as a^2 * 10^(-3), which simplifies further to a^2/1000.

Learn more about Logarithms and Exponents

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