Question

Solve the following equations.
5 ⋅ 23^(x+5) = 10240

Answer 1

The solution to the equation is x = [log(2048)/log(23)] - 5

Explanation:

Hi there!

First, let´s write the equation:

5 ⋅ 23^(x+5) = 10240

To solve for x, divide both sides of the equation by 5

23^(x+5) = 2048

Apply log to both sides of the equation

log(23^(x+5)) = log(2048)

Apply logarithm property: log(xᵃ) = a log(x)

(x + 5) log(23) = log(2048)

divide both sides of the equation by log(23)

x + 5 = log(2048)/log(23)

subtract 5 to both sides of the equation

x = [log(2048)/log(23)] - 5

The solution to the equation is x = [log(2048)/log(23)] - 5