Solve the logarithmic equation, log(base x)25 + log(base x)5 = 3, for x.
First we will combine the terms, log(base x)25*5=3 which is log(base x)125=3. Now we will change this to an exponential function, x^3=125. From here we will solve for x, and we will find that 5^3=125 so x=5.
Given the equation for a parabola, y=x^2+8x-9, take the derivative of the equation and find the slope of the line where x=11.
The derivative of the equation y'=2x+8, which will give you the slope of the parabola at any point on the line. Now plug 11 into this equation for x, y'=2(11)+8 which will give you y'=30. This means the slope of the parabola where x=11 is 30.
x^2+8x-9=0, find the solutions of x for the equations.
The equation can be factored to (x+9)(x-1)=0, from this set each factor equal to zero, x+9=0 and x-1=0. Then solve for x for each factor equal to zero. The solutions come out to be x=-9 and x=1.