Question

If log₁₀ a = m, express the following in terms of a.

10^5m−3

Answer 1

Given: log₁₀ a = m

To find: Express 10^5m−3 in terms of a.

Calculation:

Step 1: From the given relation:

log₁₀ a = m

⇒ 10^m = a

Step 2: Expand 10^5m−3:

10^5m−3 = 10^5m × 10⁻³

Step 3: Replace 10^m with a:

a⁵ = (10^m)⁵ = 10^5m

So 10^5m−3 = a⁵ × 10⁻³

`10^(5m-3) = a^5/1000`