Video: Finding the Solution Set of an Exponential Equation

Find the value of π‘₯ for which 8^(π‘₯ + 2) = 2^(π‘₯ + 4). Give your answer to the nearest tenth.

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Video Transcript

Find the value of π‘₯ for which eight to the π‘₯ plus two power equals two to the π‘₯ plus four power. Give your answer to the nearest tenth.

What we need to do is we need to somehow rewrite eight and two so that way they have the exact same base or we can rewrite eight so that actually has a base of two because eight is the same thing as two cubed. So now we can combine the three and the π‘₯ plus two for the exponents by distributing.

So now we have equal basis. And since we have equal basis, we can set their exponents equal to each other and solve. So first let’s go ahead and subtract π‘₯ from both sides of the equation. So we have two π‘₯ plus six equals four. Now I subtract six from both sides, so we have two π‘₯ equals negative two. So we need to divide by two to both sides of the equation. And we get that π‘₯ is equal to negative one.

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