Drag to combine
Use the Product Rule to combine the logarithms into a single term.
+
=
x
×
x - {{p.S}}
x(x - {{p.S}})
=
x
(x - {{p.S}})
Tap base to convert
Convert the logarithmic equation into exponential form to free the variables.
log
(x(x - {{p.S}}))
=
{{p.c}}
x(x - {{p.S}})
=
{{p.b}}
{{p.c}}
Successfully converted!
Slide to factor
Expand and solve the quadratic equation by finding the correct factors.
x² - {{p.S}}x = {{p.P}}
x² {{p.S > 0 ? '-' : '+'}} {{Math.abs(p.S)}}x - {{p.P}} = 0
(x
{{s3.val1 >= 0 ? '+' : '-'}} {{Math.abs(s3.val1)}}
)(x
{{s3.val2 >= 0 ? '+' : '-'}} {{Math.abs(s3.val2)}}
) = 0
-10Slider 110
-10Slider 210
Roots found: x = {{p.r1}} and x = {{p.r2}}
Tap roots to test
The argument of a logarithm must be positive (> 0).
Tap the candidate roots on the number line to test them in the original equation.
Term 1: x
Term 2: x - {{p.S}}
Testing x = {{s4.testingRoot}}
Term 1: x > 0
{{s4.testingRoot}} > 0
Term 2: x - {{p.S}} > 0
{{s4.testingRoot - p.S}} > 0
{{ s4.currentResult ? 'Valid Solution!' : 'Extraneous!' }}
Select a pulsing root above to test it.
🏆
Equation Solved!
The only valid solution is:
x = {{p.r1}}