How to Put Log3 243 in The Calculator

How to Calculate log₃ 243

The logarithm log₃ 243 asks the question: "To what power must 3 be raised to get 243?" Mathematically, this is expressed as:

To solve this, we need to find the exponent x that satisfies the equation 3ˣ = 243. This is where a calculator becomes very helpful.

Step-by-Step Calculation

1. First, recognize that 243 is a power of 3. Specifically, 243 = 3⁵ because:
   • 3¹ = 3
   • 3² = 9
   • 3³ = 27
   • 3⁴ = 81
   • 3⁵ = 243
2. Therefore, the equation 3ˣ = 243 simplifies to 3ˣ = 3⁵.
3. Since the bases are the same, the exponents must be equal: x = 5.

Using a Calculator to Calculate log₃ 243

While the step-by-step method works for this specific case, here's how you would use a calculator for a general logarithm calculation:

1. Enter the number you want to find the logarithm of (243).
2. Set the calculator to the logarithm function (usually labeled "log").
3. If your calculator has a base change function, select base 3.
4. If your calculator doesn't have a base change function, you can use the change of base formula:

   log₃ 243 = log₁₀ 243 / log₁₀ 3

5. Press the equals button to get the result.

For log₃ 243, the result should be 5, confirming our earlier step-by-step calculation.

Common Mistakes When Calculating Logarithms

• Using the wrong base: Always ensure your calculator is set to the correct base (3 in this case).
• Forgetting to change bases: If your calculator only has natural logarithm (ln) and common logarithm (log₁₀), use the change of base formula.
• Rounding errors: Be careful with decimal places, especially when dealing with very large or very small numbers.
• Confusing logarithm and exponential functions: Remember that log₃ 243 asks for the exponent, not the result of multiplying 3 by itself 243 times.