Questions: Solve for (y) in terms of (t). [ ln (y-43)=4 t ]

Transcript text: Solve for $y$ in terms of $t$. \[ \ln (y-43)=4 t \]

Solution

Solution Steps

To solve for $ y $ in terms of $ t $ from the equation $\ln(y - 43) = 4t$, we need to isolate $ y $. We can do this by exponentiating both sides to eliminate the natural logarithm, and then solving for $ y $.

Step 1: Understand the Problem

We are given the equation:

\[ \ln (y-43) = 4t \]

Our task is to solve for $ y $ in terms of $ t $.

Step 2: Isolate the Exponential Expression

To solve for $ y $, we need to eliminate the natural logarithm. We do this by exponentiating both sides of the equation. Recall that if $\ln(a) = b$, then $a = e^b$.

\[ y - 43 = e^{4t} \]

Step 3: Solve for $ y $

Now, we solve for $ y $ by adding 43 to both sides of the equation:

\[ y = e^{4t} + 43 \]