Solving Exponential Equations Solving Exponential Equations To solve exponential equations without logarithms, you need to have equations with comparable exponential expressions on either side of the "equals" sign, so you can compare the powers and solve. In other words, you have to have "(some base) to (some power) equals (the same base) to (some other power)", where you set the two powers equal to each other, and solve the resulting equation. For example: Solve 5x = 53. Since the bases ("5" in each case) are the same, then the only way the two expressions could be equal is for the powers also to be the same. That is: x=3 This solution demonstrates how this entire class of equation is solved: if the bases are the same, then the powers must also be the same, in order for the two sides of the equation to be equal to each other. Since the powers must be the same, then you can set the two powers equal to each other, and solve the resulting equation. Solve 101–x = 104 Since the bases are the same, I can equate the powers and solve: 1–x=4 1–4=x –3 = x Know More About :- Addition Property of Equality

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Sometimes you'll first need to convert one side or the other (or both) to some other base before you can set the powers equal to each other. For example: Solve 3x = 9. Since 9 = 32, this is really asking me to solve: 3x = 32 By converting the 9 to a 32, I've converted the right-hand side of the equation to having the same base as the left-hand side. Since the bases are now the same, I can set the two powers equal to each other: x=2 Solve 32x–1 = 27. In this case, I have an exponential on one side of the "equals" and a number on the other. I can solve the equation if I can express the "27" as a power of 3. Since 27 = 33, then I can convert and proceed with the solution: 32x–1 = 27 32x–1 = 33 2x – 1 = 3 2x = 4 x=2 As you can probably tell, you will need to get good with your powers of numbers, such as the powers of 2 up through 26 = 64, the powers of 3 up through 35 = 243, the powers of 4 up through 44 = 256, the powers of 5 up through 54 = 625, the powers of 6 up through 63 = 216, and all the squares. Warning: Don't plan to depend on your calculator for everything, because having to find every value in your calculator can waste a lot of time. You'll want to have a certain degree of facility, of familiarity and speed, by the time you reach the test, so familiarize yourself with the smaller powers now. Read More About :- Simplifying Rational Expressions

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