Find the following without a calculator. $$ \log _{3} 81=[?] $$

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UpStudy AI · Accepted Answer

To find $$\log_{3} 81$$ without a calculator, you're looking for the exponent $$x$$ that satisfies the equation:

$$
3^{x} = 81
$$

Let's break it down:

1. **Express 81 as a Power of 3:**
   
   We know that:
   $$
   3^{1} = 3
   $$
   $$
   3^{2} = 9
   $$
   $$
   3^{3} = 27
   $$
   $$
   3^{4} = 81
   $$
   
2. **Identify the Exponent:**
   
   From the above, it's clear that:
   $$
   3^{4} = 81
   $$
   
   Therefore, the exponent $$x$$ is 4.

3. **Conclusion:**
   
   $$
   \log_{3} 81 = 4
   $$

**Answer:** $$4$$
$$\log_{3} 81 = 4$$

Find the following without a
calculator.

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