Problem 2018

Solve the logarithmic equation.

log5x + log5(x+2) = log53

 

Solution:-

 

Rewrite the left side of the equation as one logarithm, using the properties of logarithms.

log5(x(x+2)) = log53

Next, exponentiate both sides of the equation.

x(x+2) = 3

Now, solve for x. Use the Distributive Property.

x2 + 2x = 3

Set the equation equal to zero.

x2 + 2x -3 = 0

Solve the resulting quadratic equation. Use the Quadratic Formula.

x = \frac{-2\pm \sqrt{16}}{2}

Remember that the domain of logmx is all x > 0, so the answer must be greater than zero.

x = \frac{-2\pm \sqrt{16}}{2}

=1

 

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