5

3 8 5 2 / | 8 0 e* =( +,x Solve: a) 21< (...

Question

3 8 5 2 / | 8 0 e* =( +,x Solve: a) 21< (

3 8 5 2 / | 8 0 e* =( +,x Solve: a) 21 < (



Answers

Solve each equation. $$ e^{2 x+5}=8 $$

Okay, so it's diaper taking the natural audible side. So this is equal to the natural log. It's now let's subtract five on both sides. So we get the notch. A log of eight minus five. And now we should divide by two. So we get the natural log of AIDS minus 5/2 is equal to that.

Okay, so we want to solve the falling for a So let's start by adding five on both sides. So this gives us that we have negative three is equal to 3/5 times a another. Unsolved for a So I'm gonna multiply by five over, agree on both sides. Okay. So we can counsel out that three, and we see that we get that a is equal to a negative five.

Okay. We gotta think about this logically. Can you take the absolute value of something and get a negative number? That is not possible. So there is no solution to this equation. Doesn't matter what you put in for acts. Once you take the square root of it, it's gonna be either zero or a positive number. There's no way it could be negative. Anything? Little negative eight.

All right. We got absolute value equations here eight times the absolute value of two X plus three are two X over three plus 10 equal zero. All right, so we have to isolate this quantity, the absolute value to expose three close 10. And we do that by dividing both sides by a It's on the right. They just disappears. We divide by eight. I'm sorry and left on the right. Zero divided by eight is still zero. So road and change anything. Also, those absolute value symbols aren't changing anything because if you take the absolute value of something and the result zero, it's because that quantity must be zero. I'm trying to say that there's only one solution to this particular absolute value equation, so I'll solve it by subtracting 10 from both sides. Um, and then I'm gonna multiply both sides by the reciprocal of 2/3. We could do this in two steps, but I'll do it and kind of one here. So two goes into 10 5 times. So our solution is gonna be negative. 573 which is negative. 15 negative. 15 is the one and only solution to this equation.


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