Solve each equation. See Examples 4–6. (1/e)^-x = (1/e^2)^(x+1)

Question

Accepted Answer

Hello, everyone we are asked to solve for X. In the given equation, the equation we are given is one divided by E raised to the negative three X power equals one divided by E cubed. All of which is raised to the two X plus five power. Our answer choices are A X equals negative 3/5 B X equals 3/5 C X equals five thirds. D X equals negative five thirds. Going back to my original equation, I'm going to rewrite my division as a fraction. So I have one over E. So one divided by E all of which is raised to the negative three X power equals the parentheses, one over E cubed. Those whole set of parentheses raise to the two X plus five power. So from here, I think the first thing I wanna do is get both of those E S out of the denominator. So I'm gonna rewrite both of these fractions with exponents. So one divided by E can be rewritten as E raise the negative first power and those parentheses are still raised to the negative three X power and that's gonna equal E raised the negative third power. Still completely raised to the two X plus five power, getting rid of the fractional piece, cleans it up a little bit. Makes it easier to see next. Recall your exponent rules. And when you have a power raised to a power, you multiply the exponents. So E raise the negative one raised to the negative three X would be E raised to the positive three X power because negative one multiplied by negative three X is a positive three X that's gonna equal E and now our exponent would be negative three, multiplied by two X plus five. So that would give us negative six X minus as our exponent. Now that we have the same base, we can compare our exponents and set them equal to each other. So we can set three X equal to negative six X minus 15. Solving for X, I'm gonna add six X to both sides. So I get nine X equals negative 15, dividing both sides by nine to get the X alone. I have X equals negative 15 9th, which can be reduced by three to negative five thirds. So our X value is that X equals negative five thirds which is answer choice. D have a nice day.

Struggling with College Algebra?

Solve each equation. See Examples 4–6. (1/e)^-x = (1/e^2)^(x+1)

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