To solve the logarithm equation, we need to rewrite it in exponential form.
The equation is:
log(x^2-2x+2) = 0
By definition, a logarithm equation can be rewritten in exponential form as:
x^2-2x+2 = 10^0
Since any number raised to the power of 0 is 1, the equation simplifies to:
x^2-2x+2 = 1
Rearranging the terms and setting the equation to zero gives:
x^2-2x+1 = 0
Now, we can solve this quadratic equation by factoring:
(x-1)(x-1) = 0
The factor theorem tells us that if the product of two factors is zero, then at least one of the factors must be zero. Therefore:
x-1 = 0
Solving for x gives:
x = 1
Therefore, the solution to the logarithm equation log(x^2-2x+2) = 0 is x = 1.
Solve the logarithm equation
Log (x^2-2x+2)=0
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1 answer