To solve this logarithmic equation, we can use the properties of logarithms to simplify it.
First, we can combine the two logarithms on the left side using the product rule for logarithms log2(4-x)(1-2x) = 2log2 3
Next, we can simplify the expression inside the logarithm on the left side log2(4-x)(1-2x) = log2 3^2
Now, we can apply the power rule for logarithms to simplify further (4-x)(1-2x) = 3^2
Expanding the left side of the equation 4 - 4x - x + 2x^2 = 9
Rearranging the terms and simplifying 2x^2 - 5x - 5 = 0
Now, we have a quadratic equation that we can solve using the quadratic formula x = [5 ± sqrt(5^2 - 4(2)(-5))] / 2(2 x = [5 ± sqrt(25 + 40)] / x = [5 ± sqrt(65)] / 4
Therefore, the solutions to the equation are x = (5 + sqrt(65)) / x = (5 - sqrt(65)) / 4
These are the values of x that satisfy the original logarithmic equation.
To solve this logarithmic equation, we can use the properties of logarithms to simplify it.
First, we can combine the two logarithms on the left side using the product rule for logarithms
log2(4-x)(1-2x) = 2log2 3
Next, we can simplify the expression inside the logarithm on the left side
log2(4-x)(1-2x) = log2 3^2
Now, we can apply the power rule for logarithms to simplify further
(4-x)(1-2x) = 3^2
Expanding the left side of the equation
4 - 4x - x + 2x^2 = 9
Rearranging the terms and simplifying
2x^2 - 5x - 5 = 0
Now, we have a quadratic equation that we can solve using the quadratic formula
x = [5 ± sqrt(5^2 - 4(2)(-5))] / 2(2
x = [5 ± sqrt(25 + 40)] /
x = [5 ± sqrt(65)] / 4
Therefore, the solutions to the equation are
x = (5 + sqrt(65)) /
x = (5 - sqrt(65)) / 4
These are the values of x that satisfy the original logarithmic equation.