Question 990797
{{{log(sqrt(x)+7) + log(2) = log(x-1)}}}

{{{log(2(sqrt(x)+7)) = log(x-1)}}}....if log same, we have

{{{2(sqrt(x)+7) = x-1}}}.......solve for {{{x}}}

{{{2sqrt(x)+14 = x-1}}}

{{{2sqrt(x) = x-1-14}}}

{{{2sqrt(x) = x-15}}}

{{{(2sqrt(x))^2 = (x-15)^2}}}

{{{4x = (x-15)^2}}}

{{{4x = x^2-30x+15^2}}}

{{{0= x^2-30x-4x+225}}}

{{{0= x^2-34x+225}}}

{{{0= x^2-9x-25x+225}}}

{{{0=( x^2-9x)-(25x-225)}}}

{{{0=x( x-9)-25(x-9)}}}

{{{0 = (x-25)(x-9)}}}

solutions:

if {{{0 = (x-25)}}}=>{{{x=25}}}
if {{{0 = (x-9)}}}=>{{{x=9}}}

solution we can use to make a statement {{{log(sqrt(x)+7) + log(2) = log(x-1)}}} true is =>{{{x=25}}}


{{{ graph( 600, 600, -5, 35, -5, 5, log(10,2(sqrt(x)+7)), log(10,(x-1))) }}}