non linear equtions

Question

solve the system

ln x = 5 ln y

log2x= 2+3 log2y

Answer 1

Assume that the non linear system of equations .

Solve the equation 1: for x.

Apply Power property of Natural logarithm : .

Apply One - to One property of Natural logarithm : If , then .

.

Substitute the value of in the equation 2: and solve for y.

Apply Quotient property of Logarithm with base a : .

Definition of logarithmic function of with base a : For .

and .

The solution .

Answer 2

Assume that the non linear system of equations .

Solve the equation 1: for x.

Apply Power property of Natural logarithm : .

Apply One - to One property of Natural logarithm : If , then .

.

Substitute the value of in the equation 2: and solve for y.

Apply Quotient property of Logarithm with base a : .

Definition of logarithmic function of with base a : For .

and .

The solution .

Assume that the non linear system of equations .

Similarly, the solutions is .