15題看不懂，請數學高手幫忙解釋的更清楚?

6^x + 4^x = 9^x
(2*3)^x + ( 2² )^x = ( 3² )^x
(2^x)(3^x) + ( 2^x )² = ( 3^x )²

令 a = 2^x , b = 3^x
ab + a² = b²
b² - ab - a² = 0

b
= [ a ± √( a² + 4a² ) ] / 2
= ( 1 ± √5 )a / 2 , 負不合, 因為 a =2^x > 0 , b = 3^x > 0
= ( 1 + √5 )a / 2

b = ( 1 + √5 )a / 2
2b = ( 1 + √5 )a
2(3^x) = ( 1 + √5 )(2^x)
兩邊取對數得 :
log 2 + x*log 3 = log ( 1 + √5 ) + x*log 2
x ( log 3 - log 2 ) = log ( 1 + √5 ) - log 2
x = [ log ( 1 + √5 ) - log 2 ] / ( log 3 - log 2 ) ≒ 1.18681439

Ans: x = [ log ( 1 + √5 ) - log 2 ] / ( log 3 - log 2 )
( ≒ 1.18681439 )

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驗算 :
6^1.18681439 + 4^1.18681439 ≒ 13.5677784
9^1.18681439 ≒ 13.5677784
故驗算無誤