Given log₁₀a = b, express 10^2b-3 in terms of a.

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Solution

Given:

log₁₀a = b

(10)^b = a ......(1 mark)

Now,

10^2b-3 = (10)^2b / (10)³

= (10^b)² / (10 × 10 × 10) .......(1 mark)

Substitute the value of (10)^b = a, we get

= a²/1000 ........(1 mark)

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