took 2^(5x) as variable U, got U^3 + U^2 - U^4 = -128 stuck here, pls halp
B BroPo New member Joined Jul 17, 2020 Messages 2 Aug 19, 2020 #1 took 2^(5x) as variable U, got U^3 + U^2 - U^4 = -128 stuck here, pls halp
H HallsofIvy Elite Member Joined Jan 27, 2012 Messages 7,763 Aug 20, 2020 #2 The "rules of exponents"are 1) (ax)(ay)=ax+y\displaystyle (a^x)(a^y)= a^{x+ y}(ax)(ay)=ax+y and 2) (ax)y=axy\displaystyle (a^x)^y= a^{xy}(ax)y=axy If U=25x\displaystyle U= 2^{5x}U=25x then U3=(25x)3=23(5x)=215x\displaystyle U^3= (2^{5x})^3= 2^{3(5x)}= 2^{15x}U3=(25x)3=23(5x)=215x. You are using the rule for 23U=(25x)(23)\displaystyle 2^3U= (2^{5x})(2^3)23U=(25x)(23), not U3\displaystyle U^3U3.
The "rules of exponents"are 1) (ax)(ay)=ax+y\displaystyle (a^x)(a^y)= a^{x+ y}(ax)(ay)=ax+y and 2) (ax)y=axy\displaystyle (a^x)^y= a^{xy}(ax)y=axy If U=25x\displaystyle U= 2^{5x}U=25x then U3=(25x)3=23(5x)=215x\displaystyle U^3= (2^{5x})^3= 2^{3(5x)}= 2^{15x}U3=(25x)3=23(5x)=215x. You are using the rule for 23U=(25x)(23)\displaystyle 2^3U= (2^{5x})(2^3)23U=(25x)(23), not U3\displaystyle U^3U3.
Steven G Elite Member Joined Dec 30, 2014 Messages 14,598 Aug 20, 2020 #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.
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.
D Deleted member 4993 Guest Aug 20, 2020 #4 BroPo said: took 2^(5x) as variable U, got U^3 + U^2 - U^4 = -128 stuck here, pls halp View attachment 21106 Click to expand... Another way (sort of): 23∗25x+22∗25x−24∗25x=−27\displaystyle 2^3 * 2^{5x} + 2^2 * 2^{5x} - 2^4 * 2^{5x} = -2^723∗25x+22∗25x−24∗25x=−27 8∗25x+4∗25x−16∗25x=−27\displaystyle 8 * 2^{5x} + 4 * 2^{5x} - 16 * 2^{5x} = -2^78∗25x+4∗25x−16∗25x=−27 −4∗25x=−27\displaystyle -4 * 2^{5x} = -2^7−4∗25x=−27 22∗25x=27\displaystyle 2^2 * 2^{5x} = 2^722∗25x=27 25x=25\displaystyle 2^{5x} = 2^525x=25 x = ?
BroPo said: took 2^(5x) as variable U, got U^3 + U^2 - U^4 = -128 stuck here, pls halp View attachment 21106 Click to expand... Another way (sort of): 23∗25x+22∗25x−24∗25x=−27\displaystyle 2^3 * 2^{5x} + 2^2 * 2^{5x} - 2^4 * 2^{5x} = -2^723∗25x+22∗25x−24∗25x=−27 8∗25x+4∗25x−16∗25x=−27\displaystyle 8 * 2^{5x} + 4 * 2^{5x} - 16 * 2^{5x} = -2^78∗25x+4∗25x−16∗25x=−27 −4∗25x=−27\displaystyle -4 * 2^{5x} = -2^7−4∗25x=−27 22∗25x=27\displaystyle 2^2 * 2^{5x} = 2^722∗25x=27 25x=25\displaystyle 2^{5x} = 2^525x=25 x = ?