What equation is the proper way to write ln 15≈2.708 in exponential form?

Question

A) 10^2.708≈15

B) 10¹⁵ = 2.708

C) e^2.708≈15

D) e¹⁵ ≈ 2.708

Answer 1

The natural logarithm (ln) has the base e. When you convert it to an exponential format, you use that value as the base of the exponential. (This eliminates options a and b, which both use base of 10).

In an exponential, you plug in the exponent and get the value. However, with logarithms, you plug in the value and get the exponent that generates it. So ln 15 ≈ 2.708 means that an exponent of 2.708 returns a value of 15. Option c shows 2.708 as the exponent and therefore is the exponential form.