In Exercises 64–73, solve each exponential equation. Where necess...

Question

In Exercises 64–73, solve each exponential equation. Where necessary, express the solution set in terms of natural or common logarithms and use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 2^(4x-2) = 64

Accepted Answer

Hello. Today we're going to be solving an exponential equation for X. So the equation given to us is three raised to the power of two X plus five equal to 81. Now one tip that's gonna help us here is the rule for the exponential equations and it states that if we have both sides of the equation with the same exponential base then we can just go ahead and set the exponents equal to each other. So that's what we're gonna do here. But if you notice on the right hand side of this equation we have a base of not three. Well keep in mind 81 could be rewritten as three raised to the fourth power. So if we rewrite this right hand side of the equation, what we get is three raised to the power of two X plus five equal to three raised to the power of four. Now both sides of this equation have the same exponential base. So we can just go ahead and set the exponents equal to each other. Doing so is going to give us two X plus five equal to four. And now we just have to sulfur X algebraic lee in order to solve for X. We're going to subtract five from both sides of this equation. That gives us two X equal to negative one. And finally what we're going to do is divide both sides equation by two and that's going to give us X equal to negative one half. And that is going to be our solution. That also means that the solution to this problem is going to be a So I hope this video helps you in understanding how to work with an exponential equation, and I'll go ahead and see you all in the next video.

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