Question

Find the value of x in the equation:

2^(3x - 1) = 16

Answer 1

x = 5/3

Explanation:

Step 1: Take the log of both sides:

log(2^(3x - 1)) = log(16)

Step 2: Apply the power rule of logs and bring down (3x - 1) on the left-hand side:

(3x - 1)(log(2)) = log(16)

Step 3: Divide both sides by log(2):

((3x - 1)(log(2)) = log(16)) / log(2)

3x - 1 = log(16) / log(2)

Step 4: Add 1 to both sides:

(3x - 1 = log(16) / log(2)) + 1

3x = (log(16) / log(2)) + 1

Step 5: Multiply both sides by 1/3 to solve for x:

(3x = log(16) / log(2)) + 1) * 1/3

x = 1/3((log(16) / log(2)) + 1)

x = 5/3

Thus, x = 5/3.