SOLUTION: I am trying to figure out how to find the value of x. 1/25=5^(x+4)

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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