In Exercises 93–102, solve each equation. 5^(x^2−12)=25^2x

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Accepted Answer

Hello. Today we're going to be solving for X in the given equation. So the equation given to us is four raised to the power of X squared minus 27 is equal to 16. Race to the power of three X. Now there is one thing that we can do to simplify this. 16 can be rewritten as four squared. So rewriting the right hand side is going to give us four to raise to the power of X squared minus 27 is equal to four raised to the power of two times three X and two times three X is going to give us six X. So on the right hand side we have four raised to the power of six X. Now, since we have two exponential values that have the same base, we can just go ahead and equate the exponential values together. So doing so is going to give us X squared minus is equal to six X. Now, since we want to sell for X we want to go ahead and set this equation equal to zero. So we're going to subtract six X to both sides of the equation. And doing this is going to give us X squared minus six. X minus 27 is equal to zero. Now this is a fact herbal trin Amiel because this try nominal factors into the quantities X minus nine times X plus three And that's going to be equal to zero. Next We're going to use our zero property and set both of the factors equal to zero. So we end up with two equations, X minus nine is equal to zero, and X plus three is equal to zero. And we need to go ahead and solve both of these on the left hand side, we can go ahead and add nine to both sides of the equation. So X is going to equal to nine, which is one of the solutions for X. And on the right hand side we can go ahead and subtract three to both sides of the equation And X is going to equal to negative three, which is the other value for X. So the values for X is x is equal to nine and X is equal to negative three. And that means that the solution to this problem is going to be a So I hope this video helps you in understanding how to solve this type of equation. And I'll go ahead and see you all in the next video.

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In Exercises 93–102, solve each equation. 5^(x^2−12)=25^2x

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