To solve this logarithmic equation, we can rewrite the expression inside the logarithm using the properties of logarithms.
Given:
2log₀,5 x = log₀,5 (2x² - x)
Using the power rule of logarithms, we can rewrite the left side of the equation:
log₀,5 x² = log₀,5 (2x² - x)
Now, since the logarithms are equal, we can drop the logarithm on both sides:
x² = 2x² - x
Simplify the equation by moving all terms to one side:
0 = x² - x
Now, factor the quadratic equation:
0 = x(x - 1)
Set each factor equal to zero:
x = 0, x = 1
Therefore, the solutions to the equation are x = 0 and x = 1.
To solve this logarithmic equation, we can rewrite the expression inside the logarithm using the properties of logarithms.
Given:
2log₀,5 x = log₀,5 (2x² - x)
Using the power rule of logarithms, we can rewrite the left side of the equation:
log₀,5 x² = log₀,5 (2x² - x)
Now, since the logarithms are equal, we can drop the logarithm on both sides:
x² = 2x² - x
Simplify the equation by moving all terms to one side:
0 = x² - x
Now, factor the quadratic equation:
0 = x(x - 1)
Set each factor equal to zero:
x = 0, x = 1
Therefore, the solutions to the equation are x = 0 and x = 1.