SOLUTION: Solve for x in the equation 5^(2x+3)-6(5^x )=595

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Question 1195396: Solve for x in the equation 5^(2x+3)-6(5^x )=595
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
5%5E%282x%2B3%29-6%285%5Ex+%29=595...........5%5E%282x%2B3%29=5%5E%282x%29%2A5%5E3+and+5%5E%282x%29=+%285%5Ex%29%5E2

%285%5Ex%29%5E2%2A5%5E3-6%285%5Ex+%29=595...........write 5%5Ex=u

u%5E2%2A125-6u=595

125u%5E2-6u-595=0......use quadratic formula

u=%28-%28-6%29%2B-sqrt%28%28-6%29%5E2-4%2A125%2A%28-595%29%29%29%2F%282%2A125%29

u=%286%2B-sqrt%2836%2B297500%29%29%2F250

u=%286%2B-sqrt%28297536%29%29%2F250

u=%286%2B-8sqrt%284649%29%29%2F250

u=+3%2F125+%2B+%284sqrt%284649%29%29%2F125

u=3%2F125+-+%284sqrt%284649%29%29%2F125

then
5%5Ex=3%2F125+%2B+%284sqrt%284649%29%29%2F125

log%285%5Ex%29=log%283%2F125+=+%284sqrt%284649%29%29%2F125%29

x%2Alog%285%29=log%283%2F125+=%284sqrt%284649%29%29%2F125%29

x=log%283%2F125+%2B+%284sqrt%284649%29%29%2F125%29%2F+log%285%29

x+=+log%283+%2B+4+sqrt%284649%29%29%2Flog%285%29+-+3


and
5%5Ex=3%2F125+-+%284sqrt%284649%29%29%2F125+has no solution in R

your solution is: x+=+log%283+%2B+4+sqrt%284649%29%29%2Flog%285%29+-+3