How do you evaluate log₃7 using the change of base formula?

To evaluate log₃7 using the change of base formula, you can convert the logarithm to a different base, typically base 10 or base e (natural logarithm). The change of base formula is expressed as:

Change of Base Formula

For any logarithm logₐb, the formula is:

logₐb = logₓb / logₓa

Here, x can be any positive number, commonly 10 or e.

Applying the Formula

For log₃7, you can choose base 10:

log₃7 = log₁₀7 / log₁₀3

Calculating the Values

• Use a calculator to find log₁₀7, which is approximately 0.8451.
• Then, find log₁₀3, which is about 0.4771.

Final Calculation

Now, divide the two results:

log₃7 ≈ 0.8451 / 0.4771 ≈ 1.77

This means that log₃7 is approximately 1.77. This method allows you to evaluate logarithms in any base by converting them to a more convenient base for calculation.