Solve each equation for the indicated variable. Use logarithms wi...

Question

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. r = p - k ln t, for t

Accepted Answer

Hey, everyone here we are asked to solve the given expression for X by making use of logarithms with proper bases. Here we are given the expression seven L is equal to Q minus three P time. The natural log of X. Here we have four answer choice options. Answer A X is equal to E raised to the power of the quantity of Q minus seven L divided by three P. Answer B X is equal to E raised to the power of three times the quantity of Q minus seven L divided by P. Answer C X is equal to E raised to the power of the quantity of seven Q minus L divided by three P. And answer D X is equal to E raised to the power of P times the quantity of Q minus seven L divided by three. So looking at our given expression in order to solve for X, we see we first need to isolate the natural log of X since it contains our variable that we are solving for. So first, we can make this three P times the natural log of X positive by simply adding this term three P times the natural log of X to both sides of the equation. And so we have three P times the natural log of X plus seven L is equal to Q. Well, as mentioned earlier, we need to isolate the natural log of X. So we first want to now subtract seven L from both sides. So we have three P times the natural log of X is equal to Q minus seven L. And so now we just need to get rid of the coefficient of the natural log. And we do this by just dividing both sides by three P. So, so far, we now have the natural log of X is equal to the quantity of Q minus seven L divided by three P. And now to get X to be outside of this natural log, we need to take E and raise it to the power of the expression on the left side and the power of the expression on the right side. So doing this, we have E raised to the power of the natural log of X is equal to E raised to the power of the quantity of Q minus seven L divided by three P. And so now on the left side of our equation, we see that E and the natural log both cancel each other out. And so we are just left with X being equal to E raised to the power of the quantity of Q minus seven L divided by three P. So with our final simplified expression, we see we have successfully solved for X from our given expression. And so we are left with answer choice A where X is equal to E raised to the power of the quantity of Q minus seven L divided by three P. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. r = p - k ln t, for t

Key Concepts

Logarithmic Functions

Isolating Variables

Natural Logarithm

Watch next