Asked by Maths whiz
Solve the logarithm equation
Log (x^2-5x+50)=2
10
Log (x^2-5x+50)=2
10
Answers
Answered by
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.
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