SOLUTION: what is the answer and the steps to this equation? (log(x-1)^2)^4+(log(x-1)^3)^2=25

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Question 450562: what is the answer and the steps to this equation?
(log(x-1)^2)^4+(log(x-1)^3)^2=25
Answer by lwsshak3(11628) About Me  (Show Source):
You can put this solution on YOUR website!
what is the answer and the steps to this equation?
(log(x-1)^2)^4+(log(x-1)^3)^2=25
..
(log(x-1)^2)^4+(log(x-1)^3)^2=25
(2log(x-1))^4+(3log(x-1))^2=25
16(log(x-1))^4+9(log(x-1))^2=25
let u=(log(x-1))^2
then u^2=log(x-1)^4
16u^2+9u=25
16u^2+9u_25=0
Solve by quadratic formula below:
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x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
..
a=16, b=9, c=-25
u=[-9ħsqrt(9^2-4*16*-25)]/2*16
u=[-9ħsqrt(1681)]/32
u=(-9ħ41)/32
u=(-9+41)/32=32/32=1
or
u=(-9-41)/32=-50/32=-1.56250 (reject)
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u=(log(x-1))^2=1
take sqrt of both sides
log(x-1)=1
convert to exponential form
10^1=x-1=10
x=11
Check:
(log(x-1)^2)^4+(log(x-1)^3)^2
(2log(x-1))^4+(3log(x-1))^
(2log(11-1))^4+(3log(11-1)^2
2log(10)^4+3log(10)^2
log(10)=1
2^4+3^2=16+9=25
..