can't figure out how to solve this

BroPo

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Jul 17, 2020
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took 2^(5x) as variable U, got U^3 + U^2 - U^4 = -128 stuck here, pls halp

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The "rules of exponents"are
1) (ax)(ay)=ax+y\displaystyle (a^x)(a^y)= a^{x+ y} and
2) (ax)y=axy\displaystyle (a^x)^y= a^{xy}

If U=25x\displaystyle U= 2^{5x} then U3=(25x)3=23(5x)=215x\displaystyle U^3= (2^{5x})^3= 2^{3(5x)}= 2^{15x}.

You are using the rule for 23U=(25x)(23)\displaystyle 2^3U= (2^{5x})(2^3), not U3\displaystyle U^3.
 
25x+3= 25x**23 = 8*25x=8U

So you should arrive at 8U + 4U - 16U = -128
-4U = -128
U= 32
25x=32. Now you solve for 5x and then x.
 
took 2^(5x) as variable U, got U^3 + U^2 - U^4 = -128 stuck here, pls halp

View attachment 21106
Another way (sort of):

2325x+2225x2425x=27\displaystyle 2^3 * 2^{5x} + 2^2 * 2^{5x} - 2^4 * 2^{5x} = -2^7

825x+425x1625x=27\displaystyle 8 * 2^{5x} + 4 * 2^{5x} - 16 * 2^{5x} = -2^7

425x=27\displaystyle -4 * 2^{5x} = -2^7

2225x=27\displaystyle 2^2 * 2^{5x} = 2^7

25x=25\displaystyle 2^{5x} = 2^5

x = ?
 
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