# Solve for x log base 256 of x<1/4

Solve for x log base 256 of x<1/4
Convert the inequality to an equality.
Solve the equation.
Rewrite in exponential form using the definition of a logarithm. If and are positive real numbers and , then is equivalent to .
Solve for .
Rewrite the equation as .
Simplify .
Simplify the expression.
Rewrite as .
Apply the power rule and multiply exponents, .
Cancel the common factor of .
Cancel the common factor.
Rewrite the expression.
Evaluate the exponent.
Find the domain of .
Set the argument in greater than to find where the expression is defined.
The domain is all values of that make the expression defined.
Use each root to create test intervals.
Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
Determine if the inequality is true.
The equation cannot be solved because it is undefined.
The left side has no solution, which means that the given statement is false.
False
False
False
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is less than the right side , which means that the given statement is always true.
True
True
Test a value on the interval to see if it makes the inequality true.
Choose a value on the interval and see if this value makes the original inequality true.
Replace with in the original inequality.
The left side is not less than the right side , which means that the given statement is false.
False
False
Compare the intervals to determine which ones satisfy the original inequality.
False
True
False
False
True
False
The solution consists of all of the true intervals.
The result can be shown in multiple forms.
Inequality Form:
Interval Notation:
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