Answer:
The solution to the equation is x = [log(2048)/log(23)] - 5
Step-by-step 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
