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You can put this solution on YOUR website!
When I first looked at your problem I thought it would be difficult. But after a few moments I realized that it is a lot easier than it looks.
\n" ); document.write( "This problem is easy because there are only three ways to raise a number to a power and get a result of 1:
- Raising a 1 to any power always results in a 1
- Raising a -1 to any even power results in a 1
- Raising any number (except zero) to the zero power results in a 1
\n" ); document.write( "Let's look at all three possibilities:
\n" ); document.write( "1) Raising 1 to a power.
\n" ); document.write( "The base in your expression is x-2. If x = 3 then the base would be a 1. And since 1 to any power is a 1, it doesn't matter what the exponent works out to be. So x = 3 is a solution to your equation.
\n" ); document.write( "2) Raising -1 to an even power.
\n" ); document.write( "The base is still x-2. If x = 1 then the base would be -1. If x = 1, would the exponent,
\n" ); document.write( "
\n" ); document.write( "Yes, if x = 1 the base is -1 and exponent is an even number. So x = 1 is another solution to your equation.
\n" ); document.write( "3) Raising a non-zero number to the zero power.
\n" ); document.write( "First let's find the x's that make the exponent,
\n" ); document.write( "
\n" ); document.write( "As a quadratic equation we will either factor this or use the Quadratic Formula. This factors fairly easily:
\n" ); document.write( "(x-4)(x+3) = 0
\n" ); document.write( "From the Zero Product Property we know that one of the factors must be zero. So:
\n" ); document.write( "x-4 = 0 or x+3 = 0
\n" ); document.write( "Solving these we find:
\n" ); document.write( "x = 4 or x = -3
\n" ); document.write( "Now we just have to make sure the base is not zero when x is one of these numbers. When x = 4, the base, x-2, is a 2. And when x = -3, the base is -5. So when x = 4 or x = -3, the exponent is zero and the base is not. So x = 4 or x = -3 are also solutions to this equation.
\n" ); document.write( "So there are four solutions to your equation:
\n" ); document.write( "x = 3 or x = 1 or x = 4 or x = -3 \n" ); document.write( "