Question

Use the change of base formula to convert log₆ 5x³ to base e.
Then evaluate when x = 4.

Answer 1

To convert log base 6 of 5x³ to base e, we use the change of base formula: log base 6 of 5x³ equals ln(5x³) divided by ln(6). When x = 4, the expression evaluates to approximately 1.543.

Step-by-step explanation:

To convert log₆ 5x³ to base e, also known as the natural logarithm (ln), we use the change of base formula:

log₆ 5x³ = ln(5x³) / ln(6)

When x = 4, we substitute this value into our expression:

log₆ 5(4)^3 = ln(5· 4³) / ln(6)

log₆ 5· 4³ = ln(320) / ln(6)

Now we can use a calculator to evaluate this expression:

ln(320) / ln(6) ≈ 2.766 / 1.792 = 1.543

The logarithmic expression in base e when x = 4 is approximately 1.543.