To solve this equation, we can first simplify it by using the properties of logarithms.
log²3 x - 4 log 3 x - 12 = 0log³(x²) - log(3^4) - 12 = 0log³(x²) - 4 - 12 = 0log³(x²) - 16 = 0log³(x²) = 16
Next, we can rewrite the equation in exponential form:
3^16 = x²x = ±√(3^16)x = ±3^8x = ±6561
Therefore, the solutions to the equation log²3 x - 4 log 3 x - 12 = 0 are x = 6561 and x = -6561.
To solve this equation, we can first simplify it by using the properties of logarithms.
log²3 x - 4 log 3 x - 12 = 0
log³(x²) - log(3^4) - 12 = 0
log³(x²) - 4 - 12 = 0
log³(x²) - 16 = 0
log³(x²) = 16
Next, we can rewrite the equation in exponential form:
3^16 = x²
x = ±√(3^16)
x = ±3^8
x = ±6561
Therefore, the solutions to the equation log²3 x - 4 log 3 x - 12 = 0 are x = 6561 and x = -6561.