Question

Solve 10^6x=93. round to the nearest ten thousand.

A) 11.8109

B) 1.0986

C) 13.3801

D) 0.3281

Answer 1

10^(6x) = 93

10⁶ˣ = 93

Take the logarithm of both sides to base 10.

Log₁₀ 10⁶ˣ =Log₁₀ 93

6x * (Log₁₀ 10) = Log₁₀ 93

6x = (Log₁₀ 93) / (Log₁₀ 10)

By laws of logarithm Log₁₀ 10 = 1

6x = (Log₁₀ 93) / 1

6x = Log₁₀ 93 With Calculator Log₁₀ 93 ≈ 1.9685

6x ≈ 1.9685

x ≈ 1.9685/6

x ≈ 0.3281

Option D.

Hope this explains it.