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Use the values ln 4 ≈ 1.3 and ln 50 ≈ 3.9 to find the approximate value of log₄ 50.

User Neta Meta
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Final answer:

The approximate value of log₄ 50 is found using the change of base formula and given values for natural logarithms, yielding an approximate value of 3.

Step-by-step explanation:

To find the approximate value of log₄ 50, we can use the change of base formula, which is log₄ 50 = ln 50 / ln 4. We have been given that ln 4 ≈ 1.3 and ln 50 ≈ 3.9. Using these values, we approximate log₄ 50 by dividing 3.9 by 1.3, which gives us:

log₄ 50 ≈ 3.9 / 1.3 ≈ 3

This means that log₄ 50 is approximately 3, reflecting that 50 is close to the cube of 4 (4³ = 64), so the logarithm is a bit less than 3 since 50 is a bit less than 64.

To approximate the value of log₄ 50, the change of base formula is applied: log₄ 50 = ln 50 / ln 4. Given ln 4 ≈ 1.3 and ln 50 ≈ 3.9, the calculation becomes log₄ 50 ≈ 3.9 / 1.3 ≈ 3. This approximation signifies that log₄ 50 is approximately 3, indicating the proximity of 50 to the cube of 4 (4³ = 64).

The logarithm is slightly less than 3 since 50 is slightly less than 64. This application of the change of base formula offers a practical method for estimating logarithmic values.

User Perry
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