Answer: x=20104
Step-by-step explanation:To solve this equation, we need to use the properties of logarithms and exponents. Here are the steps:
First, we can rewrite the equation using the power rule of logarithms: log20x3−2logx=4⇔log20x3=4+2logx
Next, we can rewrite the equation using the product rule of logarithms: log20x3=4+2logx⇔log20x3=logx2+log104
Then, we can rewrite the equation using the quotient rule of logarithms: log20x3=logx2+log104⇔logx220x3=log104
Now, we can simplify the equation by canceling out the common factors: logx220x3=log104⇔logx20x=log104⇔log20=log104
Finally, we can solve the equation by applying the inverse function of logarithm: log20=log104⇔10log20=10log104⇔20=104⇔x=20104
Therefore, the solution to the equation is x=20104
