How Do You Start Solving a Logarithmic Equation?

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To solve the logarithmic equation Log2 (x^2 - x - 2) = 2, recognize that if Log2 (z) = 2, then z equals 2^2, which is 4. This means you can set the argument of the logarithm equal to 4, leading to the equation x^2 - x - 2 = 4. Rearranging gives x^2 - x - 6 = 0, which can be factored or solved using the quadratic formula. The solutions for x will be the values that satisfy this equation. Understanding the property of logarithms where the base cancels with the exponent is key to starting the solution.
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Homework Statement


Solve the logarithmic equation for x:
Log2 (x^2 - x - 2) = 2

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The Attempt at a Solution



I'm just totally lost on how to even start...
 
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Hint: if : Log2 (z) = 2, then z=2^2=4.
 
Solved it. Totally forgot that if you put log base 2 as the power of 2, they cancel!
 

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