Solve for t or y, as appropriate.
-$$e ^ { ( \ln 0.3 ) t } = 0.6$$
A) $\frac { \ln 0.6 } { \ln 0.3 }$
B) 2
C) $\ln 2$
D) $\frac { e ^ { 0.6 } } { \ln 0.3 }$

Question

Quizplus · Accepted Answer

Using the property of logarithms that $\log_a b^c = c\log_a b$, we can rewrite the left-hand side of the equation as $e^{(\ln 0.3)t} = (e^{\ln 0.3})^t = 0.3^t$.

So, we have $0.3^t = 0.6$.

We want to solve for $t$. Taking the natural logarithm of both sides, we get $\ln 0.3^t = \ln 0.6$. Again using the property of logarithms mentioned above, we can simplify this to $t\ln 0.3 = \ln 0.6$. Solving for $t$, we get:

$$t = \frac{\ln 0.6}{\ln 0.3}$$

Therefore, the answer is A).

Solve for T or Y, as Appropriate e(ln⁡0.3)t=0.6e ^ { ( \ln 0.3 ) t } = 0.6e(ln0.3)t=0.6

Solve for T or Y, as Appropriate $e ^ { ( \ln 0.3 ) t } = 0.6$