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