Pregunta
Solve for
in the equation below.
Round your answer to the nearest hundredth.
Do not round any intermediate computations.
Round your answer to the nearest hundredth.
Do not round any intermediate computations.
Ask by Olson Smith. in the United States
Mar 11,2025
Solución de inteligencia artificial de Upstudy
Respuesta verificada por el tutor
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Solución
We start with the equation
Step 1. Take the natural logarithm of both sides:
Step 2. Use the logarithm power rule,
, to bring the exponent down:
Step 3. Solve for
by dividing both sides by
:
Subtract 8 from both sides:
Step 4. Evaluate
using calculator approximations for the logarithms. We have
Thus,
Now substitute back into the equation for
:
Step 5. Round the answer to the nearest hundredth:
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Como
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Mind Expander
To solve the equation
, we can start by applying logarithms to both sides. Using the natural logarithm (though any logarithm would work) gives us:
Using the property of logarithms that allows us to bring the exponent down, we have:
Now, divide both sides by
:
Next, we isolate
by subtracting 8 from both sides:
Now we can calculate
and
:
Substituting these values in gives us:
Calculating the fraction:
So now we have:
Finally, rounding to the nearest hundredth:

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