SOLUTION: (a) (4x+2)(2x) = 32 (b) (3x+2)(9x+3) = 81 (c) log (x-3) + log (x) = 1 (d) log2 (x2 – 6x) = 3 + log2 (1-x)

Algebra ->  Equations -> SOLUTION: (a) (4x+2)(2x) = 32 (b) (3x+2)(9x+3) = 81 (c) log (x-3) + log (x) = 1 (d) log2 (x2 – 6x) = 3 + log2 (1-x)       Log On


   

Question 161945: (a) (4x+2)(2x) = 32
(b) (3x+2)(9x+3) = 81
(c) log (x-3) + log (x) = 1
(d) log2 (x2 – 6x) = 3 + log2 (1-x)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first two to get you started

1)

%284x%2B2%29%282x%29+=+32+ Start with the given equation


8x%5E2%2B4x+=+32+ Distribute


8x%5E2%2B4x-32=0 Subtract 32 from both sides


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=8, b=4, and c=-32


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%284%29+%2B-+sqrt%28+%284%29%5E2-4%288%29%28-32%29+%29%29%2F%282%288%29%29 Plug in a=8, b=4, and c=-32


x+=+%28-4+%2B-+sqrt%28+16-4%288%29%28-32%29+%29%29%2F%282%288%29%29 Square 4 to get 16.


x+=+%28-4+%2B-+sqrt%28+16--1024+%29%29%2F%282%288%29%29 Multiply 4%288%29%28-32%29 to get -1024


x+=+%28-4+%2B-+sqrt%28+16%2B1024+%29%29%2F%282%288%29%29 Rewrite sqrt%2816--1024%29 as sqrt%2816%2B1024%29


x+=+%28-4+%2B-+sqrt%28+1040+%29%29%2F%282%288%29%29 Add 16 to 1024 to get 1040


x+=+%28-4+%2B-+sqrt%28+1040+%29%29%2F%2816%29 Multiply 2 and 8 to get 16.


x+=+%28-4+%2B-+4%2Asqrt%2865%29%29%2F%2816%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-4%2B4%2Asqrt%2865%29%29%2F%2816%29 or x+=+%28-4-4%2Asqrt%2865%29%29%2F%2816%29 Break up the expression.


x+=+%28-1%2Bsqrt%2865%29%29%2F%284%29 or x+=+%28-1-sqrt%2865%29%29%2F%284%29 Reduce


So the answers are x+=+%28-1%2Bsqrt%2865%29%29%2F%284%29 or x+=+%28-1-sqrt%2865%29%29%2F%284%29


which approximate to x=1.766 or x=-2.266







2)

%283x%2B2%29%289x%2B3%29+=+81+ Start with the given equation


27x%5E2%2B27x%2B6+=+81+ FOIL


27x%5E2%2B27x%2B6-81=0 Subtract 81 from both sides


27x%5E2%2B27x-75=0 Combine like terms.


Notice we have a quadratic equation in the form of ax%5E2%2Bbx%2Bc where a=27, b=27, and c=-75


Let's use the quadratic formula to solve for x


x+=+%28-b+%2B-+sqrt%28+b%5E2-4ac+%29%29%2F%282a%29 Start with the quadratic formula


x+=+%28-%2827%29+%2B-+sqrt%28+%2827%29%5E2-4%2827%29%28-75%29+%29%29%2F%282%2827%29%29 Plug in a=27, b=27, and c=-75


x+=+%28-27+%2B-+sqrt%28+729-4%2827%29%28-75%29+%29%29%2F%282%2827%29%29 Square 27 to get 729.


x+=+%28-27+%2B-+sqrt%28+729--8100+%29%29%2F%282%2827%29%29 Multiply 4%2827%29%28-75%29 to get -8100


x+=+%28-27+%2B-+sqrt%28+729%2B8100+%29%29%2F%282%2827%29%29 Rewrite sqrt%28729--8100%29 as sqrt%28729%2B8100%29


x+=+%28-27+%2B-+sqrt%28+8829+%29%29%2F%282%2827%29%29 Add 729 to 8100 to get 8829


x+=+%28-27+%2B-+sqrt%28+8829+%29%29%2F%2854%29 Multiply 2 and 27 to get 54.


x+=+%28-27+%2B-+9%2Asqrt%28109%29%29%2F%2854%29 Simplify the square root (note: If you need help with simplifying square roots, check out this solver)


x+=+%28-27%2B9%2Asqrt%28109%29%29%2F%2854%29 or x+=+%28-27-9%2Asqrt%28109%29%29%2F%2854%29 Break up the expression.


So the answers are x+=+%28-27%2B9%2Asqrt%28109%29%29%2F%2854%29 or x+=+%28-27-9%2Asqrt%28109%29%29%2F%2854%29


which approximate to x=1.24 or x=-2.24