Solve the exponential equation algebraically Approximate the

Solution

given e^5x = e^{x^2-14}

equate respect tive powers

5x =x²-14

x²-5x-14=0

x²-7x+2x-14=0

x(x-7)+2(x-7)=0

(x-7)(x+2)=0

x+2=0,x-7=0

x=-2, x=7