Given:
The logarithmic expression is:
To find:
The equivalent expression of given expression by using change-of-base formula.
Solution:
The change-of-base formula is:
The given expression is:
Using the change-of-base formula, we get
Where, is a constant and c>0.
Let , then
Therefore, the correct option is a.
Answer:
a) -4
b) 1
c) 1
Step-by-step explanation:
a) The matrix A is given by:
to find the eigenvalues of the matrix you use the following:
where lambda are the eigenvalues and I is the identity matrix. By replacing you obtain:
and by taking the determinant:
and the roots of this polynomial is:
hence, the real eigenvalue of the matrix A is -4.
b) The multiplicity of the eigenvalue is 1.
c) The dimension of the eigenspace is 1 (because the multiplicity determines the dimension of the eigenspace)