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DETAILS MY NOTES STITZPRECALC3 6.4.011. PREVIOU
Solve the following equation analytically. (Enter your answers as a comma-separated list.)
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Solve the following equation analytically. (Enter your answers as a comma-separated list.)
Additional Materials
Ask by Riley Howell. in the United States
Mar 22,2025
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Tutor-Verified Answer
Answer
Solution
Solve the equation
.
Solve the equation by following steps:
Solve the equation by following steps:
- step0: Solve for
:
- step1: Find the domain:
- step2: Simplify:
- step3: Convert the logarithm into exponential form:
- step4: Evaluate the power:
- step5: Transform the expression:
- step6: Check if the solution is in the defined range:
- step7: Find the intersection:
The solution to the equationis .
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Mind Expander
To solve the equation
, first, isolate the logarithm by multiplying both sides by -1, giving you
. To eliminate the logarithm, rewrite it in exponential form:
. Evaluating this gives approximately
or in scientific notation,
.
If you’re wondering what to watch out for when solving logarithmic equations, remember that the argument of a logarithm must always be positive. So,
must always be greater than zero for the logarithm to be defined!