Question

Solve the logarithm equation
Log (x^2-5x+50)=2
10

Answer 1

To solve the logarithm equation, we need to get rid of the logarithm by converting it to exponential form.

The exponential form of logarithm equation is:

log(base a) x = b is equivalent to a^b = x

Using this, we can rewrite the given equation as:

10^2 = x^2 - 5x + 50

Simplifying the equation:

100 = x^2 - 5x + 50

Moving all terms to one side:

x^2 - 5x + 50 - 100 = 0

x^2 - 5x - 50 = 0

Now, we can solve this quadratic equation by factoring or using the quadratic formula.

Factoring:

(x - 10)(x + 5) = 0

Setting each factor to zero and solving for x:

x - 10 = 0 or x + 5 = 0

x = 10 or x = -5

So, the solutions to the logarithm equation are x = 10 or x = -5.