Elizabeth’s problem of the week solution no. 2
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The graphs of y=log2(x) and y=x-2 intersect at one point, x=2. The document provides a 4 step solution: 1) set the equations equal, 2) move the exponent, 3) use logarithm rules, 4) solve for x and discard the extraneous solution, leaving x=2 as the only point of intersection.
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Elizabeth’s problem of the week solution no. 2
- 1. Elizabeth’s Problem of the Week Solution May 3rd, 2010
- 2. In how many points do the graphs of and intersect?
- 3. Step One Set the two equations equal to each other.
- 4. Step Two Move the 2 in the first equation back into the exponent.
- 5. Step Three Use the rules of logarithms to find that…
- 6. Step Four Solve for x. The solution x=0 does not fit into the domain of logarithmic functions, so it can be discarded, leaving only x=2. or
- 7. Final Answer The graphs only intersect at ONE point, when x=2.