Functions, graphs and inverses, question 19

A student solves the equation below as shown. Find the first line that is wrong.

\log(x + 2) + \log(x - 1) = \log 4

$\log\bigl((x + 2) + (x - 1)\bigr) = \log 4$
Adding logarithms adds what is inside them.
$2x + 1 = 4$
Equal logarithms have equal arguments.
$x = \tfrac{3}{2}$
Solve the linear equation.
$\tfrac{3}{2} > 1,\ \text{so both logarithms are defined.}$
Check the domain: x + 2 > 0 and x − 1 > 0 need x > 1.

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