Solve the following equations.
3 ⋅ 2^5x = 216

Solution: x = log(72) / (5 log(2)) = 1.233985

Step-by-step explanation:

Hi there!

We have the following equation:

3 ⋅ 2^5x = 216

to solve for x, divide first both sides of the equation by 3

2^5x = 72

Apply log to both sides of the equation

log(2^5x) = log(72)

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

5x · log(2) = log(72)

divide both sides of the equation by 5 · log(2)

x = log(72) / (5 log(2))

Let´s check the solution:

3 ⋅ 2^5x = 216

3 · 2^5(log(72) / (5 log(2))) = 216

3 · 2^(log(72) / log(2)) = 216

3 · 72 = 216

216 = 216

Then x = log(72) / (5 log(2)) = 1.233985 is a solution of the equation