Solve each exponential equation in Exercises 1–22 by expressing e...

Question

Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 2^x=64

Accepted Answer

Hello, today we're gonna be solving for X in the following exponential equation. So what we are given is three to the power of X equal to 2187. Now we have a property for exponents that states if we have two exponential values that contain the same base, then we can just set the exponents equal to each other. So in this example, we have a race to the power of B equal to a race to the power of C. Since both of these exponential values have the same base A, we're going to set the exponents equal to each other and rewrite this statement as B is equal to C and this is going to be the idea that we want to use in order to sell for X in our exponential equation. Now, one thing to note about the right hand side is that 2187 can be rewritten as three race to the power of a number can be rewritten as three race to the power of seven. And if we substitute this exponential value into the right hand side of the equation. What we are left with is three to the power of X equal to three to the power of seven. Notice that both of the exponential values have the same base of three. And that means we can just set the exponents equal to each other. And doing so is going to give us X is equal to seven which is going to be the value of X that we are looking for. And with that being said, the answer to this problem is going to be B so I hope this video helps you in understanding how to approach this problem. And I'll go ahead and see you all in the next video.

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Solve each exponential equation in Exercises 1–22 by expressing each side as a power of the same base and then equating exponents. 2^x=64

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