Date: 01/22/2001 at 15:44:12 From: Crystal Price Subject: Find x How do you do a problem like this? Use your knowledge of powers and the properties of exponents to find the value of x in the equation 8^x + 2 = 2.
From: Doctor Ian Subject: Re: Find x Hi Crystal, Let's take a look at that equation: 8^x + 2 = 2 As usual, we want to combine as many numbers as we can, so we can subtract 2 from each side of the equation: 8^x + 2 - 2 = 2 - 2 8^x = 0 Now we have a problem. Recall that 8^1 = 8, and 8^0 = 1, and 8^(1/n) is some root of 8, so it's always greater than zero. The problem is that there is NO way that you can raise a positive number to any exponent to get zero. So this leads me to believe that you really meant to say 8^(x+2) = 2 When you're using '^' to write exponents that involve more than just a number, you _need_ to use parentheses. That is, x+2 8 = 8^(x+2) 8^x+2 = (8^x) + 2 Anyway, let's look at 8^(x+2) = 2 It turns out that 2 is the cube root of 8; that is, 2^3 = 8 2 = 8^(1/3) So we can use this information: 8^(x+2) = 2 = 8^(1/3) This tells us that x + 2 = 1/3 Why? Just as you can add or subtract the same thing to/from both sides of an equation, or multiply both sides by the same thing, you can also raise both sides of an equation to the same exponent - or, if both sides are the same base raised to an exponent, you can drop the base. All that's saying is that if you have a^b = a^c then you know that b = c. Does that make sense? Anyway, if you solve x + 2 = 1/3 you'll get the value of x that makes 8^(x+2) = 2 a true statement. I hope this helps. Let me know if you'd like to talk about this some more, or if you have any other questions. - Doctor Ian, The Math Forum http://mathforum.org/dr.math/
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