Final Answer:
The value of x that satisfies the equation log(6)⁴x² - log(6)x = 2 is x ≈ 0.195.
Step-by-step explanation:
To solve this equation, we first isolate the variable term:
log(6)⁴x² - log(6)x = 2
log(6)⁴x² = log(6)x + 2
Next, we take the antilog of both sides to remove the logarithms:
6⁴x² =
* 10²
We can simplify the right side by using the properties of logarithms:
6⁴x² =
* 100
Now, we can separate the variables and solve for x:
x = (log(100) - log(6⁴)) / log(6)
Using a calculator or statistical software, we can approximate the value of x as x ≈ 0.195. This means that if we substitute x = 0.195 into the original equation, the left side and right side will be equal within a certain level of accuracy.