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horsena [70]
3 years ago
5

Solve for the equation of value of x(show your solution)

Mathematics
1 answer:
sertanlavr [38]3 years ago
7 0

Answer:

2. ) {25}^{2x} - 1 = {125}^{3x} + 4

=> {25}^{2x} = {125}^{3x} + 4 +1

=> {(5)^(2)}^{2x} = {(5)^(3)}^{3x} + {5}^{1}

=> {5}^{4x} = {5}^{9x} + {5}^{1}

=> 4x = 9x + 1

=> 4x - 9x = 1

=> - 5x = 1

=> x = 1/-5

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100 ---> 96 is -4

96 ---> 104 is +8

104 ---> 88 is -16

88 ---> 120 is +32

120 ---> 56 is -64  

So first we go down by 4, then up by 8, then down 16, then up 32, then finally down 64.  

The pattern of numbers is: -4, +8, -16, +32, -64  

Notice it's the powers of 2:  

2^2 = 4

2^3 = 8

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each term doubles. Also each term alternates in sign. One is positive, then the next is negative and so on.  

The last difference is -64, which doubles to -128. Change the sign to positive to get +128  

Add 128 to the last term of 56 to get

128+56 = 184  

Therefore, the final answer is 184

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