# Determine one variableIf ln t= -ln2 what is t ?

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have ln t= - ln 2

Now we can write -ln 2  as -1* ln 2

use the property a*ln b = ln b^a

=> ln 2^(-1) = ln (1/2)

As ln t = ln (1/2), we get t = 1/2

Therefore we have t = 1/2

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

ln t = - ln 2

We will preview the properties of the logarithm equations.

We know that: ln a^b = b*ln a

Then we will rewrite the equation.

- ln 2 = -1 * ln 2 = ln 2^-1 = ln (1/2)

==> ln t = ln (1/2)

Now we have the logarithms are equal, then t= 1/2

Then the answer is t = 1/2

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

First of all, we'll impose the constraints of existence:

t>0

ln t= -ln2

We'll use the power property of logarithms:

ln t = ln 2^-1

ln t = ln 1/2

Since the bases are matching, we'll use the fact that the logarithmic function is injective and we'll get:

t = 1/2 > 0