Determine one variableIf ln t= -ln2 what is t ?
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
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
First of all, we'll impose the constraints of existence:
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