Solve each equation. Give solutions in exact form. See Examples 5...

Question

Solve each equation. Give solutions in exact form. See Examples 5–9. log(3x + 5) - log(2x + 4) = 0

Accepted Answer

Hey, everyone. Here we are asked to solve the logarithmic equation for X and provide an exact solution here. The given equation is log of seven X plus nine minus log of 20 plus six X is equal to zero. Here we have four answer choice options, answer A, the solution set of negative five and 11. Answer B, the solution set of four answer C the solution set of 11 and answer D the solution set of zero. Here, our first step in solving this given equation for X is to just move this negative log of 20 plus six X from the left side of the equation to the right side. And we can do this by simply adding log of 20 plus six X to both sides of our equation. And so in doing this, we can rewrite our equation as log of seven X plus nine is equal to log of plus six X. Now, in our rewritten equation, we see both sides of the equation have the log of some expression. And so we want to get rid of this logarithm and we can do this by having 10, be set to the power of the expression on the left side and then having 10 be set to the power of the expression on the right side of the equation. So doing this, we see that the 10 and the logarithm both cancel out. So now we are left with seven X plus nine is equal to, to 20 plus six X. Now we just need to solve this equation for X. So we can first just subtract nine from both sides and we get seven X is equal to 11 plus six X. And now getting our X terms on the same side of the equation, we can subtract six X from both sides. And we see we end up with just X being equal to 11. So here we have our value of X as 11 and therefore our solution set just contains the value of 11. So here we are left with answer choice C where again we have the solution set of 11. 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. Give solutions in exact form. See Examples 5–9. log(3x + 5) - log(2x + 4) = 0