If log_10(x^2-3x+6)=1, the value of x is:

1953 AMC 12 Problem 21

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21.

\log_{10}(x^2-3x+6)=1,

the value of

x

is:

10

2

4

-2

3

-1

4

-1

none of these

Convert the logarithmic equation to

x^2-3x+6=10

Factor the resulting quadratic

The logarithmic equation is equivalent to

x^2-3x+6=10,

\begin{aligned} x^2-3x-4&=(x-4)(x+1)\\ &=0. \end{aligned}

Thus

x=4

x=-1.

The correct answer is D.