Solve for x using Logarithm4^x+6^x =9^x

1 answer:

7 0

4^x + 6^x = 9^x

4^x + 6^x - 9^x = 0

2^2x + (2×3)^x - 3^2x = 0

2^2x + 2^x×3^x - 3^2x = 0

(⅔)^2x + (⅔)^x - 1 = 0

let t = ( ⅔)^x

t² + t - 1 = 0

t = (-1+√5 ) / 2

(⅔)^x = (-1+√5 ) / 2

x = Log base ⅔ ((-1+√5 ) / 2 )

x = 1.18681

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