125^9x-2 = 150

A) -1.8847
B) -0.1069
C) 0.3375
D) 1.0378

1 answer

To solve for x, we need to isolate x by taking the logarithm of both sides.

Starting with the equation:
125^9x-2 = 150

Take the natural logarithm of both sides:
ln(125^9x-2) = ln(150)

Apply the power rule of logarithms:
(9x-2)ln(125) = ln(150)

Calculate ln(125) and ln(150):
(9x-2)(4.8283) = 5.0106

4.8283(9x-2) = 5.0106
43.4547x - 9.6566 = 5.0106

Add 9.6566 to both sides:
43.4547x = 14.6672

Divide by 43.4547 to solve for x:
x ≈ 0.3375

Therefore, the answer is:

C) 0.3375