SOLUTION: please help me solve this equation (1)SOLVE FOR X (a){{{300^(2x+5)=1}}} (b){{{2^(x+2)5^(6-x)=1000}}}

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: please help me solve this equation (1)SOLVE FOR X (a){{{300^(2x+5)=1}}} (b){{{2^(x+2)5^(6-x)=1000}}}       Log On


   

Question 1104283: please help me solve this equation
(1)SOLVE FOR X
(a)300%5E%282x%2B5%29=1
(b)2%5E%28x%2B2%295%5E%286-x%29=1000
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
(1)SOLVE FOR X
(a)300%5E%282x%2B5%29=1
300^(2x+5) = 1
(2x+5)*log 300 = 0
2x+5 = 0
x = -5/2
---------------------------
(b)2%5E%28x%2B2%29%2A5%5E%286-x%29=1000
-----
2^(x+2)* 5^(6-x) = 1000
-----
Take the log of both sides to get:
(x+2)*log2 + (6-x)*log5 = 3
-------------------------------------
[log(2)-log(5)]x + 2log(2) + 6log(5) = 3
----------------------------------
[log(2/5)]x = 3-log4+log5^6
-0.3979x = 6.5918
x = -16.56..
Cheers,
Stan H.
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Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
please help me solve this equation
(1)SOLVE FOR X
(a)300%5E%282x%2B5%29=1
-------------
2x+5 = 0
x = -5/2
===================
2%5E%28x%2B2%295%5E%286-x%29=1000
(x+2)*log(2) + (6-x)*log(5) = 3
x*log(2) + log(4) + log(5^6) - x*log(5) = 3
etc