12^x-5 = 12^3x
find x
To find x, we can first simplify the equation by subtracting 12^3x from both sides:
12^x - 12^3x = 5
Next, we can attempt to factor out a common term to simplify further. Notice that both terms have 12^x in common, so we can factor that out:
12^x(1 - 12^(2x)) = 5
Now, we can divide both sides by (1 - 12^(2x)):
12^x = 5 / (1 - 12^(2x))
We can now solve for x by taking the logarithm of both sides. Let's take the logarithm base 12:
log12(12^x) = log12(5 / (1 - 12^(2x)))
x = log12(5 / (1 - 12^(2x)))
Unfortunately, there is no simple way to algebraically solve for x in this equation.