Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
x>0
Alternative Form
x∈(0,+∞)
Evaluate
2ln(x)=ln(x2)
Find the domain
More Steps
Evaluate
{x>0x2>0
Calculate
More Steps
Evaluate
x2>0
Since the left-hand side is always positive or 0,and the right-hand side is always 0,the statement is true for any value of x,except when x2=0
x2=0
The only way a power can be 0 is when the base equals 0
x=0
Exclude the impossible values of x
x=0
{x>0x=0
Find the intersection
x>0
2ln(x)=ln(x2),x>0
Evaluate
2ln(x)−ln(x2)=0
Rewrite the expression
ln(x)×0=0
Any expression multiplied by 0 equals 0
0=0
The statement is true for any value of x
x∈R
Check if the solution is in the defined range
x∈R,x>0
Solution
x>0
Alternative Form
x∈(0,+∞)
Show Solution
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