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#