This problem is from MGMAT 4^a + 4^a+1 = 4^a+2 - 176 OA is a=2 but I don't understand the arithmetic please help

ejager wrote:This problem is from MGMAT 4^a + 4^a+1 = 4^a+2 - 176 OA is a=2 but I don't understand the arithmetic please help 4^(a+2) - 4^(a+1) - 4^a = 176. In other words: 176 = difference between 3 CONSECUTIVE POWERS OF 4. List the powers of 4: 4, 16, 64, 256... The next greatest power of 4 will be too great (over 1000). Test the 3 greatest values in the list above: 256-64-16 = 176. Success! Since 4^a = 16, a=2.

ejager wrote: 4^a + 4^(a+1) = 4^(a+2) - 176 Here's another approach: 4^a + 4^(a+1) = 4^(a+2) - 176 Rearrange to get variables on one side: 4^(a+2) - 4^(a+1) - 4^a = 176 Factor out 4^a to get: (4^a)(4² - 4¹ - 1) = 176 Evaluate part in brackets: (4^a)(16 - 4 - 1) = 176 Simplify: (4^a)(11) = 176 Divide both sides by 11 to get: 4^a = 16 Solve: a = 2 Cheers, Brent

176 = 4^a+2 -4^a-4^a+1 176 = 4^a(16-4-1) 176 = 11* 4^a 4^a = 16 a= 2

ejager wrote:This problem is from MGMAT 4^a + 4^a+1 = 4^a+2 - 176 OA is a=2 but I don't understand the arithmetic please help Another Approach Question : 4^a + 4^(a+1) = 4^(a+2) - 176 i.e. 4^a + (4^a x 4) = 4^a x (4^2) - 176 Let 4^a = X now the equation reduces to X + 4X = 16X -176 i.e. 11X = 176 i.e. X = 16 i.e. 4^a = 16 i.e. a =2

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