Question 410543: I am trying to figure out how to find the value of x.
1/25=5^(x+4)
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! your equation is:
1/25 = 5^(x+4)
take the log of both sides of this equation to get:
log(1/25) = log(5^(x+4))
since log (a^b) =b*log(a), then if you let 5 = a and you let (x+4) = b, then you get:
log(1/25) = (x+4)*log(5)
divide both sides of this equation by log(5) to get:
x+4 = log(1/25) / log(5)
subtract 4 from both sides of this equation to get:
x = log(1/25) / log(5) - 4
solve by using your calculator to get:
x = -6
your answer should be x = -6
when x = -6, the equation of:
1/25 = 5^(x+4) becomes:
1/25 = 5^(-6+4) which becomes:
1/25 = 5^(-2) which becomes:
1/25 = 1/5^2 which becomes:
1/25 = 1/25
this confirms the answer is correct.
the answer is x = -6.
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