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Solve the following equation algebraically for the variable a. Write your answer in exect fonn (no decimal approximations). (13 points)2a 6y a-3y bgl bgl bg 3 Sa+8 ...

Question

Solve the following equation algebraically for the variable a. Write your answer in exect fonn (no decimal approximations). (13 points)2a 6y a-3y bgl bgl bg 3 Sa+8 Ta

Solve the following equation algebraically for the variable a. Write your answer in exect fonn (no decimal approximations). (13 points) 2a 6y a-3y bgl bgl bg 3 Sa+8 Ta



Answers

Solve each equation. Give the exact solution and an approximation to four decimal places. See Example 3. $$ 13^{x-1}=2 $$

We're being asked to solve the given equation. So as you can see we have an exponential equation. So there's lots of ways to solve. But the first thing you should try and do is see if you can rewrite both the left and right hand side with the same base. So I'm going to focus on the right hand side. Well I know that 27 is equal to three to the third power. So let's substitute that meaning we would have three to the X squared minus 12 power equal to 1/3 to the third. Well now we have to get rid of that fraction. But remember according to our negative exponent rule, if we have 1/8 to the end, that's equal to eight to the negative end power. So to move this to the numerator we can rewrite it as three to the negative third. So now we have three to the X squared minus 12 equal to three to the negative third. Well now both the left hand and right hand side have the same base which means that our exponents will equal to each other. So in other words will have x squared minus 12 equal to negative three. And now we just have to solve the given equation. So first we'll add 12 to both sides. Negative three plus 12 is nine. So X squared equals nine. And then we'll take the square with both sides. And don't forget when you do that, you have to put your plus or minus symbol. Well the square the nine is equal to three. Perfect. We have two solutions X could equal to plus or -3.

The question says that we have to solve the given equation for the specified variable. The question is X. To the power to buy three plus Y. To the power to buy three equals to eight to the power to buy three. And we have to solve it for why? Now moving towards the solution, the given equation can be written on us. X. to the power to buy three Plus by 20 power to buy three. It wants to eight to the power to buy three is the given equation. So you can write a task by to the power to buy three equals to eight to the power to buy three minus X. To the power to buy three. Now raise the governing equation to the power three by two. You will get y to the power to buy three to the power three by two equals to a to the power to buy three minus X. To the power to buy three to the power freeway. Here you will get by equals to eight to the power to buy three minus X. To the power to buy three to the power they like to. And let's go with the solution to the human question. Thank you.

Alright. In this video we'll be looking at an equation that has a lot of variables in it and we're solving for a very specific variable. Alright. So in this video we are looking at this question here, it's gonna be X. To the two thirds plus. Why? To the two thirds is equal to aid the two thirds. Oops. And then this question we're solving for Y. So the first I want to do is isolate the term that has the Y. In it. That would be the Y. Two the two thirds. So it's being added to exit the two thirds. So first I wanna do is attract exit the two thirds to isolate that wide term. All right, So I'm getting y equal to two thirds. Whoops. Why? To the two thirds? Alright. Is equal to eight of the two thirds minus. Excellent, two thirds. All right. So now we can see that wise by itself and the next thing you do is get rid of that two thirds, explain it on the wine. And the best way to do that is to raise it to a certain power. That will eliminate the two thirds. So we're gonna look at the reciprocal of two thirds. Remember reciprocal is the flip version of that fraction. The reciprocal would be three halves because if I take two thirds times three halves I get one right because these would cross out and that's the whole point. I just want wider the first. All right. So that's gonna do next I'm gonna raise both sides to three halves. So notice on the left hand side. These when crossing out to become a once we have wider the first all right and then the right hand side. We really can't do anything else with that. I can't individually raise these terms of the three halves because of the minus sign in between. If there's a multiplication sign then yes I could do that. But um one of the laws of exponents, there's not a law that we can do raise everything to the three has power some power if there's a subtraction addition sign. So because I have the situation was going to leave this alone, so we have y equal to parentheses, eight of the two thirds minus X. The two thirds. I'm raising the three halves and I can't combine the A. To the two thirds minus exited to third because they have different bases. Okay so this will be my final answer right here.

Okay, so we would solve the falling for X. Let's start particular that your log of both sides. So yet Jack's natural laws of three is equipped in a natural law of 14. And now let's divide both to on the natural log of three amble sides to solve for X. Okay, so this gives us that X is equal to a natural law of fortune over in that dialogue of three times to. Now, let's plug this into our cast waiting. Okay, so we see that this is approximately 1.2 barrel. What?


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