Algebra
Calculus
Trigonometry
Matrix
Question
Solve the equation
x=ln(kπ),k∈Z
Alternative Form
x=ln(180∘k),k∈Z
Evaluate
−sin(ex)×ex=0
Elimination the left coefficient
sin(ex)×ex=0
Separate the equation into 2 possible cases
sin(ex)=0ex=0
Solve the equation
More Steps
Evaluate
sin(ex)=0
Use the inverse trigonometric function
ex=arcsin(0)
Calculate
ex=0
Add the period of kπ,k∈Z to find all solutions
ex=kπ,k∈Z
Solve the equation
More Steps
Evaluate
ex=kπ
Take the logarithm of both sides
ln(ex)=ln(kπ)
Evaluate the logarithm
x=ln(kπ)
x=ln(kπ),k∈Z
x=ln(kπ),k∈Zex=0
Since the left-hand side is always positive,and the right-hand side is always 0,the statement is false for any value of x
x=ln(kπ),k∈Zx∈/R
Solution
x=ln(kπ),k∈Z
Alternative Form
x=ln(180∘k),k∈Z
Show Solution
