Exponential and Logarithmic FunctionsFind: log 2 ⁡ ( x 2 − 4 x − 28 ) = 2

Question

Exponential and Logarithmic FunctionsFind:       log    2    ⁡  (      x    2    −  4  x  −  28  )  =  2

Phiplyrhypelw0 · Accepted Answer

Problem: We need to solve for x in the given equation

\log_{2} (x^{2} - 4 x - 28) = 2

Remember that if

\log_{a} (b) = y

, then

a^{y} = b

. In our equation, a=2,

b = x^{2} - 4 x - 28

, and y=2. Therefore

x^{2} - 4 x - 28 = 2^{2} = 4

. This is easy to solve for.

x^{2} - 4 x - 28 = 4

x^{2} - 4 x - 32 = 0

Factor it

(x - 8) (x + 4) = 0

x = 8, - 4

Karley Castillo · Accepted Answer

log    2    ⁡  (      x    2    −  4  x  −  28  )  =  2    ⟹        x    2    −  4  x  −  28  =      2    2    =  4      x    2    −  4  x  −  32  =  0  (  x  −  8  )  (  x  +  4  )  =  0  x  =  8  ,     −  4

Exponential and Logarithmic Functions Find: log_2(x^2−4x−28)=2

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