1. PROVE:
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2. The very first thing you need to do is to make the Great
Wall of China.
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3. A good strategy is to always work on the most
complicated side. In this case, it is the LHS.
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4. First, we need to prove that the base is equal to
the argument.
BASE
ARGUMENT
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5. I'm going to start simplifying the base first.
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6. Since both terms have a different denominator we
have to multiply each term to a term that is equal to
1 in order to achieve a common denominator.
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7. Simplify the whole expression
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8. Now, since both terms have the same denominator, we
can just write them into a single term.
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9. Simplify both the numerator and denominator
once more.
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10. Can you spot the Pythagorean Identity on the
numerator?
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11. Do some algebraic massage
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12. Now that we are done simplifying the base, let us
simplify the argument.
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13. Since both terms have a different denominator we
have to multiply each term to a term that is equal to
1 in order to achieve a common denominator.
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14. Simplify the whole expression.
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15. Now, since both terms have the same denominator, we
can just write them into a single term.
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16. Simplify the numerator.
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17. Can you spot the Pythagorean Identity on the
numerator?
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18. Do some algebraic massage
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19. Now, we've proven that the base is equal to the
argument. This means that whatever the
logarithm is, it is equal to the exponent on the
base of the argument.
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20. Now we need to prove this:
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21. Bring out the Great Wall of China and start
working on the more complicated side.In this
instance it is the RHS.
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22. Factor out the RHS.
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23. Do you recognize the Pythagorean Identity?
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24. Do some algebraic massage using the
pythagorean identity.
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25. Apply a little bit more tweaking.
QED
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