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How do you solve this equation? Does it contain log?
7^7x = 7^x+25
and
log ( x + 9 ) + log ( x + 6 ) = 1
1 Answer
- Yves From CanadaLv 61 decade agoFavorite Answer
7^7x = 7^x+25
If it is :
7^(7x) = 7^(x+25)
that means :
7x = x + 25
7x - x = 25
6x = 25
x = 25/6
log ( x + 9 ) + log ( x + 6 ) = 1
Since log(A*B) = log(A) + log(B)
log[(x+9)*(x+6)] = 1
log(x^2+15x+54) = 1
antilog(log(x^2+15x+54)) = antilog(1)
x^2 + 15x + 54 = 10
x^2 + 15x + 44 = 0
You can factor (x + 4)(x + 11)
x = -4 and x = -11
We reject x = -11 because that would cause a log of a negative number.
Answer is x = -4
PROOF :
log ( x + 9 ) + log ( x + 6 ) = 1
log(-4 + 9) + log(-4 + 6) = 1
log(5) + log(2) = 1
0.69897 + 0.30103 = 1
1 = 1 :ok
