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How to Put Log_ 6 216 on A Calculator Ti-83

Reviewed by Calculator Editorial Team

Calculating logarithms with different bases on a TI-83 calculator requires understanding how to change the base. This guide explains how to input and solve log₆ 216 using the TI-83's built-in functions.

How to Calculate log₆ 216

The logarithm log₆ 216 represents the exponent to which the base 6 must be raised to obtain 216. To calculate this on a TI-83 calculator, you'll use the change of base formula:

log₆ 216 = log₂ 216 / log₂ 6

This formula allows you to use the TI-83's built-in logarithm function (which calculates natural logarithms) by converting the problem to a common base.

Step-by-Step Guide

  1. Enter the logarithm function

    Press the [MATH] key and select option 2: log. This enters the log function.

  2. Input the argument

    Enter the number 216 (the argument of the logarithm).

  3. Enter the division operator

    Press the [÷] key to enter the division operator.

  4. Enter the second logarithm

    Press [MATH] again and select option 2: log. Then enter the number 6.

  5. Calculate the result

    Press [ENTER] to calculate the result. The TI-83 will display the value of log₆ 216.

Formula Used

The change of base formula for logarithms is:

logₐ b = logₖ b / logₖ a

Where:

  • a is the new base (6 in our case)
  • b is the argument (216 in our case)
  • k is the common base (2 in our case, using the TI-83's log function)

The TI-83's log function calculates natural logarithms (base e). Using base 2 provides a convenient common base for the calculation.

Worked Example

Let's calculate log₆ 216 step by step:

  1. Calculate log₂ 216 ≈ 7.415
  2. Calculate log₂ 6 ≈ 2.585
  3. Divide the results: 7.415 / 2.585 ≈ 2.868

Therefore, log₆ 216 ≈ 2.868.

The exact value of log₆ 216 is approximately 2.86807 when calculated with more precision.

FAQ

Why can't I just use the log function directly on the TI-83?
The TI-83's log function calculates natural logarithms (base e). To calculate logarithms with other bases, you need to use the change of base formula.
What if I want to calculate log₆ 216 using natural logarithms?
You can use the formula: log₆ 216 = ln 216 / ln 6. Press [MATH] and select option 3: ln for natural logarithms.
How accurate is the result on the TI-83?
The TI-83 provides approximately 10 decimal places of precision for logarithm calculations.
Can I use the TI-83's calculator for more complex logarithmic problems?
Yes, the same change of base formula applies to any logarithmic calculation with different bases.