can't figure out how to solve this

[BroPo]

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

 

[HallsofIvy]

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

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

You are using the rule for \(\displaystyle 2^3U= (2^{5x})(2^3)\), not \(\displaystyle U^3\).

 

[Steven G]

2^5x+3= 2^5x**2³ = 8*2<sup>5x=8U

So you should arrive at 8U + 4U - 16U = -128
-4U = -128
U= 32
25x=32. Now you solve for 5x and then x.</sup>

 

[Deleted member 4993]

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):

\(\displaystyle 2^3 * 2^{5x} + 2^2 * 2^{5x} - 2^4 * 2^{5x} = -2^7\)

\(\displaystyle 8 * 2^{5x} + 4 * 2^{5x} - 16 * 2^{5x} = -2^7\)

\(\displaystyle -4 * 2^{5x} = -2^7\)

\(\displaystyle 2^2 * 2^{5x} = 2^7\)

\(\displaystyle 2^{5x} = 2^5\)

x = ?