Question

solve Log2 x^_5x+14=3​

Answer 1

Example: Solve log2 (x + 1) +log2 (x) = 1.

The first step is to use properties of logarithms to combine the logarithmic terms. Using product rule we get:

log2 ((x + 1)x) = 1 or log2 (x2 + x) = 1
which is the same as

x2 + x = 21 or x2 + x - 2= 0.
This is a quadratic equation, and you can easily solve it. The solutions of this last equation are

x = 1 and x = -2
BUT NOTE!! ONLY x = 1 is a solution of the original equation! x = -2 cannot be a solution, because you can't take logs of negative numbers, so if you try to put x = -2 into the original logarithmic equation you would get

log2 (-2 + 1) +log2 (-2) = 1
Neither logarithm makes sense, so -2 can't be a solution.

This is the tricky part of solving logarithmic equations: noticing and eliminating those pesky numbers that appear when you try to solve a given equation, which are not solutions. Remember, it is perfectly possible for a logarithmic equation not to have any solutions.
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