2^5+2^5+3^5+3^5+3^5=? A) 5^6 B) 13^5 C) 2^6+3^6 D) 2^7+3^8 E) 4^5+9^5

paresh_patil wrote:2^5+2^5+3^5+3^5+3^5=? A) 5^6 B) 13^5 C) 2^6+3^6 D) 2^7+3^8 E) 4^5+9^5 What we really have here is an algebra question involving the combining of like terms. First, notice that K + K = 2K Using the same logic, 2^5 + 2^5 = 2(2^5) = (2^1)(2^5) = 2^6 Similarly, notice that M + M + M = 3M Using the same logic, 3^5 + 3^5 + 3^5 = 3(3^5) = (3^1)(3^5) = 3^6 So, 2^5 + 2^5 + 3^5 + 3^5 + 3^5 = 2^6 + 3^6 Answer: C Cheers, Brent

Brent- then how do I tackle this one: 2^x-2^(x-2)=3(2^13) x=?

2^x-2^(x-2)=3(2^13) x=? I can take this: 2^x(1-2^(-2))=3*(2^13) 2^x(1-1/4))=3*(2^13) 2^x(3/4)=3*(2^13) The first part: 2^x(3/4) = 2^x(3/(2^2)) = 3*(2^x/2^2) = 3*2^(x-2) I hope the last passage is clear... 3*2^(x-2)=3*(2^13) divide by 3 2^(x-2)=(2^13) x=15

paresh_patil wrote:Brent- then how do I tackle this one: 2^x-2^(x-2)=3(2^13) x=? This requires some factoring. 2^x - 2^(x-2) = 3(2^13) 2^(x-2)[2^2 - 1] = 3(2^13) 2^(x-2)[3] = 3(2^13) So, 2^(x-2)= 2^13 x-2 = 13 [spoiler]x = 15[/spoiler] Cheers, Brent

When you post a problem, please include the answer choices. 2^5+2^5+3^5+3^5+3^5=? A) 5^6 B) 13^5 C) 2^6+3^6 D) 2^7+3^8 E) 4^5+9^5 An alternate approach is to BALLPARK. 2� = 32. 3� = 3(3�) = 3*81 ≈ 250. Thus: 2� + 2� + 3� + 3� + 3� = 2(32) + 3(250) ≈ 60+750 ≈ 800. Since 3� ≈ 250, 3� ≈ 750. Thus, the only viable answer choice is C.

paresh_patil wrote: then how do I tackle this one: 2^x-2^(x-2)=3(2^13) x=? When you post a question, please include the answer choices. If 2^X - 2^(X-2) = 3 x 2^17, What is the value of X? A. 16 B. 17 C. 18 D. 19 E. 20 We can plug in the answers, which represent the value of X. Answer choice C: 18. 2^18 - 2^(18-2) = 3 * 2^17 2^18 - 2^16 = 3 * 2^17 2*16(2^2 - 1) = 3 * 2^17 2^16 * 3 = 3 * 2^17. Doesn't work. Eliminate C. To match 2^17 on the right side of the equation, the exponent on the left side of the equation needs to be increased by 1. The correct answer is D. Answer choice D: 19. 2^19 - 2^(19-2) = 3 * 2^17 2^19 - 2^17 = 3 * 2^17 2*17(2^2 - 1) = 3 * 2^17 2^17 * 3 = 3 * 2^17.