SOLUTION: 1.solve for x log4 x^5=-1 2.solve for x in terms of k log9 x + log9(x+9)=k x=? find x if k = 10

Question 271879: 1.solve for x
log4 x^5=-1
2.solve for x in terms of k
log9 x + log9(x+9)=k
x=?
find x if k = 10

Answer by dabanfield(803) (Show Source): You can put this solution on YOUR website!
1.solve for x
log4 x^5=-1
2.solve for x in terms of k
log9 x + log9(x+9)=k
x=?
find x if k = 10
1.) log (base 4) x^5 = -1 so
5*log (base 4) x = -1
log (base 4) x = -1/5 so by definition of the log then
4^(-1/5) = x
2.) log9 x + log9 (x+9) = k so
log9 (9*(x+9)) = k so by definition of a log:
9^k = 9*(x+9)
9^k = 9x + 81
9x = 9^k-81
x = 9^k/9-(81/9)
x = 9^(k-1) - 9
When k = 10 then x = 9^(10-1)- 9
x = 9^9 - 9

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