document.write( "Question 450562: what is the answer and the steps to this equation?
\n" ); document.write( "(log(x-1)^2)^4+(log(x-1)^3)^2=25 \n" ); document.write( "
Algebra.Com's Answer #310024 by lwsshak3(11628)\"\" \"About 
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what is the answer and the steps to this equation?
\n" ); document.write( "(log(x-1)^2)^4+(log(x-1)^3)^2=25
\n" ); document.write( "..
\n" ); document.write( "(log(x-1)^2)^4+(log(x-1)^3)^2=25
\n" ); document.write( "(2log(x-1))^4+(3log(x-1))^2=25
\n" ); document.write( "16(log(x-1))^4+9(log(x-1))^2=25
\n" ); document.write( "let u=(log(x-1))^2
\n" ); document.write( "then u^2=log(x-1)^4
\n" ); document.write( "16u^2+9u=25
\n" ); document.write( "16u^2+9u_25=0
\n" ); document.write( "Solve by quadratic formula below:
\n" ); document.write( "..
\n" ); document.write( "\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"
\n" ); document.write( "..
\n" ); document.write( "a=16, b=9, c=-25
\n" ); document.write( "u=[-9ħsqrt(9^2-4*16*-25)]/2*16
\n" ); document.write( "u=[-9ħsqrt(1681)]/32
\n" ); document.write( "u=(-9ħ41)/32
\n" ); document.write( "u=(-9+41)/32=32/32=1
\n" ); document.write( "or
\n" ); document.write( "u=(-9-41)/32=-50/32=-1.56250 (reject)
\n" ); document.write( "..
\n" ); document.write( "u=(log(x-1))^2=1
\n" ); document.write( "take sqrt of both sides
\n" ); document.write( "log(x-1)=1
\n" ); document.write( "convert to exponential form
\n" ); document.write( "10^1=x-1=10
\n" ); document.write( "x=11\r
\n" ); document.write( "\n" ); document.write( "Check:
\n" ); document.write( "(log(x-1)^2)^4+(log(x-1)^3)^2
\n" ); document.write( "(2log(x-1))^4+(3log(x-1))^
\n" ); document.write( "(2log(11-1))^4+(3log(11-1)^2
\n" ); document.write( "2log(10)^4+3log(10)^2
\n" ); document.write( "log(10)=1
\n" ); document.write( "2^4+3^2=16+9=25
\n" ); document.write( ".. \n" ); document.write( "
\n" );