Question

Convert ln(16) = -2x into exponential form.

Answer 1

The exponential form is:
`e^(-2x)` = 16

Explanation:

In(16) = -2x

The natural logarithm (In) is the inverse of the exponential function,

i.e In
`e^(b)` = b

Thus, find the exponential function of both sides;

In(16) = -2x

e In(16) = e (-2x)

⇒ 16 =
`e^(-2x)`

i.e
`e^(-2x)` = 16

So that;

`(1)/(e^(2x) )` = 16

Answer 2

`e^(-2x)=16`

Explanation:

For logarithmic equations:

`Log_(a)x=b $ is equivalent to a^b=x, x>0, a>0, a\\eq -1`

In ln(16) = -2x

Ln is the natural logarithm, and:

a= e

x=16

b=-2x

Therefore, in exponential form, the equivalent form is:

`e^(-2x)=16`