4(5^(2(x+2)) = 3-25(5^x)?

4 * 5^[ 2(x+2) ] = 3 - 25*5^x = 3 - 5^(x+2)

令 u = 5^(x+2)
4u^2 = 3 - u
4u^2 + u - 3 = 0
( 4u - 3 )( u + 1 ) = 0
u = 3/4 , - 1 ( 不合, 因為 u > 0 )

5^(x+2) = 3/4
等式兩邊取自然對數, 等式恆成立:
(x+2) * ln 5 = ln 3 - ln 4
x+2 = ( ln 3 - ln 4 ) / ln 5
x = [ ( ln 3 - ln 4 ) / ln 5 ] - 2 ..... Ans

4(5^(2(x+2)) = 3-25(5^x)
4(5^2x)(5^4)=3-25(5^x)
2500(5^2x)+25(5^x)-3=0
5^x=0.03 or 5^x=-0.04(rej.)
x=-2.18

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