"Solving the Exponential Equation: 4^x + 16^x = 272 | Algebra Trick Explained! - video Dailymotion

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Transcript

00:00Let's solve the equation which is 4 to the power x plus 16 to the power x is equal to 272 and let's

00:09solve this for the sake of value of x. Since 4 to the power x can be as it is plus and 16 can be

00:18written in the form of 4 square and whole to the power x is equal to 272. We can write 4 square

00:27whole to the power x is equal to 4 to the power x whole to the power 2 means that power and its power

00:34we can change both of their places. So we can let that 4 to the power x is equal to y. Substituting

00:43both of these values in the above equation that becomes y plus y square is equal to 272. Y square

00:52can be in the first term so that becomes y square plus y is equal to 272. 16 times 17 is equal to 272.

01:05So we can simply factorize the above quadratic equation in y. So the above equation will be

01:11y square plus 17y minus 16y is equal to 272. When 272 comes to next side that becomes negative of 272.

01:24And the equation is y square plus 17y minus 16y minus 272 is equal to 0. Then y is common in first two terms

01:35so that becomes y times y plus 17y minus 16y minus 17y minus 17y minus 17ymah and y plus 17y minus

01:52and so y plus 17y minus 17 times y minus 17y is equal to 0. here are two cases y plus 17y minus 17y equals to 0.

01:59is equal to 0 so then y is equal to minus 17 other case is y minus 16 is equal to 0

02:08so y is equal to 16 that's the second answer since when by our substitution that 4 to the

02:19power x is equal to y so y is equal to 16 three terms are equal to each other so means that first

02:25and second first and third can also be equal to each other so 4 to the power x is equal to 16 and

02:3216 can be in the form of 4 square so that is 4 to the power x is equal to 4 square here we'll use the

02:39algebraic property which is if a to the power m is equal to a to the power n so their power will be

02:46equal to each other means that bases are same so x is equal to 2 is the first answer is equal to 17

02:53so we will use that also 4 to the power x is equal to y and y is equal to 17 that can't be

03:02y can't be equal to 17 because that 4 to the power x can can't become that one 17 so that's the solution

03:11thanks for watching