Question

Use the method from the Example to approximate the solution to the equations below to two decimal places.

5^x = 1,000

Answer 1

The approximate solution of the equation is 4,29.

Explanation:

The solve of this fomula is:

5ˣ = 1000

You can use log in each side of the formula::

log₁₀ 5ˣ = log₁₀ 1000

By logarithm law (logₐ (mⁿ) = n logₐ m. And as log₁₀(1000) = 3:

x log₁₀ 5 = 3

x = 3 / log₁₀ 5

x ≈ 4,29

Thus, the approximate solution of the equation is 4,29.

I hope it helps!