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. log A = log B - C log x, for A

Accepted Answer

Hey, everyone here we are asked to make use of logarithms with proper base to solve the given expression for P. Here, the given expression is log of P is equal to log of two Q minus three R times log of X. Here we have four answer choice options. Answer A P is equal to Q divided by two times X raised to the power of three R. Answer B P is equal to two Q times X raised to the power of three R. Answer C P is equal to two Q to divided by X raised to the power of three R. And answer D P is equal to two divided by Q times X raised to the power of three R. So here to solve this expression for P, we want to begin by reducing the right side as much as possible. And we can begin by reducing the last term of the right side which is three R times log of X. And we can reduce this term by recalling the logarithmic identity which states that X times log of A is equivalent to log of a raise to the power of X. So now utilizing this formula for this last term. On the right side, we can rewrite our equation as log of P is equal to log of two Q minus log of X raised to the power of three R. And so now we can further reduce the expression on the right side of our equation by recalling another logarithmic property, which states that the log of A minus log of B is equivalent to log of A divided by B. And so now utilizing this formula to simplify the right side of our equation, our equation becomes log of P is equal to log of two Q divided by X raised to the power of three R. And so now we see both sides of our equation have a logarithm. And so we want to cancel out the logarithm. And since this log does not have an identified base, we assume that this log is of base 10. And so because it is of base 10, we can raise or have 10 be raised to the power of both sides of the equation. And so rewriting our equation we have on the left side is raised to the power of log of P and this is equal to the right side which is now 10 raised to the power of log of two Q divided by X raised to the power of three R. And so now we see on both sides of our equation that the logarithm and 10 cancel out. And so we are left with P is equal to two Q all divided by X raised to the power of three R. And so with our final expression, we have solved for P and so we are left with answer choice C where again we have P is equal to two Q all divided by X raised to the power of three R. 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. log A = log B - C log x, for A

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