Question

Number 9. Emulate the logarithm using the change of base formula. Round you result to three decimal places.

Log3(14)

Answer 1

Explanation:

To emulate the logarithm using the change of base formula, we need to use a base that is more convenient to evaluate. Let's use base 10:

log3(14) = log10(14) / log10(3)

Using a calculator, we can evaluate the numerator and denominator:

log10(14) ≈ 1.146

log10(3) ≈ 0.477

Dividing the numerator by the denominator gives:

log3(14) ≈ 2.402

Rounding to three decimal places, the final result is:

log3(14) ≈ 2.402

Answer 2

Log3(14)

= log(14) / log(3) (Change of base formula)

= 4 / 1.965 (log(3) = 1.965)

= 2.041 (rounded to 3 decimal places)

2.041