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. A = P (1 + r/n)^(tn), for t

Accepted Answer

Hey, everyone here we are asked to make use of logarithms with proper bases to solve the given expression for X. Here we are given M is equal to R times the quantity of A divided by B plus one range to the power of X times Y. Here we have four answer choice options. Answer A X is equal to log of R divided by M divided by the quantity of Y times log of A divided by B plus one answer B X is equal to log of M divided by R divided by the quantity of Y times log of A divided by B plus one. Answer C X is equal to log of M divided by R divided by the quantity of Y times log of B divided by A plus one. And answer D X is equal to Y times log of M divided by R all divided by log of eight, divided by B plus one. So here to begin solving this expression for X, we first want to move this coefficient of R to the left side of the equation. So we simply need to divide both sides by R. So here we have M divided by R is equal to the quantity of A divided by B plus one raised to the power of X times Y. So now to work to get this X term to be outside of the exponent, we simply have to take the log of both sides. So taking the log, we have log of M divided by R is equal to the log of the quantity of A divided by B plus one raised to the power of X times Y. So from here, we have to recall the logarithmic property which states that the log of a raised to the power of X is equivalent to X times log of A. So now utilizing this formula to simplify the right side of our equation, we have that log of M divided by R is equal to the quantity of X times Y times log of A divided by B plus one. So now to get X alone, we simply divide both sides of the equation by this larger expression here, the quantity of Y times log of A divided by B plus one. And again, we divide both sides by this expression. And so now we see that X will be alone. And our simplified expression is X is equal to the log of M divided by R all divided by the quantity of Y times log of A divided by B plus one. And so we have solved our given equation for X and we are left here with answer choice B where again, we have X is equal to log of M divided by R divided by the quantity of Y times log of A divided by B plus one. Thanks for watching. I hope you found this video helpful and I'll see you again next time.

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Solve each equation for the indicated variable. Use logarithms with the appropriate bases. See Example 10. A = P (1 + r/n)^(tn), for t