I get x=621. Take log(base 5) of both side and bring down the exponent to get sqrt2 * log(x+4)= sqrt8 * log25 where log is log base 5 so that log25=2. Therefore log(x+4)=sqrt(8)*2/sqrt(2)=4, and so x+4=5^4=625 giving us x=621.
However, if you consider negative square roots (like â25 = 5 OR -5), then â8 can be broken down to +-2â2 (since -2â2 times -2â2 also equals â8).
(x+4)^â2 = 25^â8
(x+4)^â2 = 25^(-2â2)
(x+4)^â2 = (25^-2)^â2
(x+4)^â2 = (1/(25^2))^â2
(x+4)^â2 = (1/625)^â2
x+4 = 1/625
x+4-4 = (1/625)-4
x = (1/625)-4
x = (1/625)-(2500/625)
x = -2499/625
Answer: 621 (but technically there is a second answer which is -2499/625)
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Verified answer
I get x=621. Take log(base 5) of both side and bring down the exponent to get sqrt2 * log(x+4)= sqrt8 * log25 where log is log base 5 so that log25=2. Therefore log(x+4)=sqrt(8)*2/sqrt(2)=4, and so x+4=5^4=625 giving us x=621.
(x+4)^â2 = 25^â8
(x+4)^â2 = 25^(â4â2)
(x+4)^â2 = 25^(2â2)
(x+4)^â2 = (25^2)^â2
(x+4)^â2 = 625â2
x+4 = 625
x+4-4 = 625-4
x = 621
However, if you consider negative square roots (like â25 = 5 OR -5), then â8 can be broken down to +-2â2 (since -2â2 times -2â2 also equals â8).
(x+4)^â2 = 25^â8
(x+4)^â2 = 25^(-2â2)
(x+4)^â2 = (25^-2)^â2
(x+4)^â2 = (1/(25^2))^â2
(x+4)^â2 = (1/625)^â2
x+4 = 1/625
x+4-4 = (1/625)-4
x = (1/625)-4
x = (1/625)-(2500/625)
x = -2499/625
Answer: 621 (but technically there is a second answer which is -2499/625)