9 to the power x = 27 to the power y, 64 to the powerxy = 152 to the power x+1?

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solve the simutaneous equation

Madie Hilpert · Accepted Answer

9^x = 27^ybecomes(3^2)^x = (3^3)^y 3^(2x) = 3^(3y)so… 2x = 3yy = 2x/364^(xy) = 152^(x+1) (2^6)^(xy) = (152^x)(152)2^(6xy) = 152(152^x)ln 2^(6xy) = ln 152(152^x)6xy (ln 2) = ln 152 + ln 152^x6xy (ln 2) = ln 152 + x ln 152Plug in y = 2x/36x(2x/3) (ln 2) = ln 152 + x ln 1524x^2 ln 2 – x ln 152 – ln 152 = 0using quadratic formula…a = 4 ln 2b = -ln 152c = -ln 152This becomes quite a mess. Do you have all the information typed correctly?============================Did you mean 512, instead of 152?64^xy = 512^(x+1)(2^6)^xy = (2^9)^(x+1)2^(6xy) = 2^(9(x+1))so6xy = 9(x+1)Now you have two simpler equations…y = 2x/3 and6xy = 9(x + 1)solve by substitution… 6x(2x/3) = 9x + 94x^2 = 9x + 94x^2 – 9x – 9 = 0(4x + 3)(x – 3) = 0x = -3/4 and 3Plug those into y = 2x/3 to find y…so…(3, 2) and (-3/4 , -1/2)are the two answers.

Madie Hilpert · Answer

If you put 9 and 27 as powers of 3 you will have:(3^2)^x=(3^3)^y Which you can then turn into:3^2x=3^3y And then using like bases, you have:2x=3y Where you can solve for x (because solving for y would give you a yucky fraction) and you have:x=1.5yIf you put 64 and 152 as powers of…hmmm, they don’t have a common base. Okay, replace the x’s with the formula we got above. This would give you: 64^(1.5y^2) = 152^(1.5y+1) Then take the logs of both sides, this would give you:(1.5y^2)(log64)=(1.5y+1)(log 152) Subtract to get 0 on right side of eqn, and you would get:(1.5y^2)(log64)-(1.5y+1)(log 152)=0Then solve with graphing calculator or even quadratic formula.With a graphing calc, I got the answers:y = -.4777334 & y = 1.6857213And then find x by multiplying y by 1.5 and you have the corresponding x vaules of:x=-.7166001 & x=2.52858195

Madie Hilpert · Answer

if 9^x = 27^y… You can do a logarithm of both sides:xln9 = yln27 ln9 = ln3^2=2ln3, ln27 = ln3^3=3ln3so y =2/3x64^xy = 152^(x+1) thenxyln64 = (x+1)ln152. since y =2/3x2/3x^2ln64 = (x+1)ln152. 64=2^6 so ln64 = 6ln2. Your equation becomes:4ln2*x^2 -ln152*x -ln152 = 0Now I am assuming you meant 512 and not 152.ln512 = ln2^9 = 9ln2.Your equation becomes :4ln2*x^2 -9ln2*x -9ln2 = 0 , divide by ln2:4x^2 -9x -9 = 0 which is solved as :(x-3)(4x+3)=0 :x=3 or x =-3/4.since a^x is only possible for positive values of x, then x=3y=2/3x, so y=2

Madie Hilpert · Answer

9 X 27

Madie Hilpert · Answer

9^x=27^y => 3^2x=3^3y => 2x=3y =>6y=4x.64^xy=152^(x+1) (!?) =>2^(6yx)=152^(x+1) =>2^(4x^2)=152^(x+1) and … solution must be determine roughly!

Madie Hilpert · Answer

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Kelsie Sawayn

9 to the power x = 27 to the power y, 64 to the powerxy = 152 to the power x+1?

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