Question
Solve the logarithm equation
Log (x^2-5x+50)=2
10
Log (x^2-5x+50)=2
10
Answers
GPT 3.5
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.
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.