Question

If log₁₀ a = m, then 10^3m+1 in terms of a is ______.

Options

• 1000^a

• 1000 a³

• 100 a

• 10 a³

Answer 1

If log₁₀ a = m, then 10^3m+1 in terms of a is 10 a³.

Explanation:

Given: log₁₀ a = m

To find: Express 10^3m+1 in terms of a.

Calculation:

Step 1: Express a in terms of m:

Since log₁₀ a = m, we know:

a = 10^m

Step 2: Simplify 10^3m+1:

10^3m+1 = 10^3m × 10¹

= (10^m)³ × 10

= a³ × 10

∴ 10^3m+1 = 10 a³