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3.5 Solving Logarithmic Equations: Worked Examples |
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Example 1. Solve for |
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Use the
definition of logarithm to convert to exponential form: |
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Check: |
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Example 2. Solve for |
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Use the definition of logarithm to
convert to exponential form: |
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This is now an exponential equation, write both |
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sides with the same base:
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Check: |
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Example 3. Solve
for |
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Use the definition of logarithm to
convert to exponential form: |
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Check:
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Example 4. Solve
for |
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Use the definition of logarithm to
convert to exponential form: |
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Solve the quadratic:
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Check:
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Example 5. Solve for |
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As the natural logs of the two different
expressions are equal, we have: |
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Solve the quadratic equation:
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Check: |
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