Solve the equation ? With steps please

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Answer 1 · 2017-11-03T08:34:39

$x = 3$ or $x = 4$

$log_2(x^2 - 7x + 14) = 1$

Rearrange the equation to remove the log function
$x^2 - 7x + 14 = 2^1$

Simplify
$x^2 - 7x + 12 = 0$

Now to solve the quadratic
the b term $( -7)$ is negative and the constant $(12)$ is positive

so both the factors of the constant must be negative

$3$ and $4$ multiply to give $12$ and add to give $7$
therefore
$(x-3)(x-4) = 0$

$x = 3$ or $x = 4$