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Question

If $$\log_{10} (x^{2} - 3x + 6) = 1$$, the value of $$x$$ is


A
10 or 2
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B
4 or 2
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C
3 or 1
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D
4 or 1
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E
None of these
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Solution

The correct option is B $$4$$ or $$-1$$
Given: $$\log_{10}(x^2-3x+6)=1$$

$$\log_{10}(x^2-3x+6)=\log_{10}10$$.......$$(1)$$            [since $$\log_aa=1$$]

From $$(1)$$:

$$x^2-3x+6=10$$

$$\Rightarrow x^2-3x-4=0$$

$$\Rightarrow (x-4)(x+1)=0$$

$$\Rightarrow x=-1\ or\ 4$$

But we should also check that $$f(x)=x^2-3x+6>0 $$ for $$x=-1,4$$........[for 

$$\log_aN$$; $$N>0$$]

$$f(-1)=(-1)^2-3(-1)+6=10>0$$

$$f(4)=4^2-3(4)+6=10>0$$

Hence both values are satisfying the condition.

So, $$x=-1,4$$


Mathematics

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