Instructions: find x

Equation: log base 2[(4.3^x)-6]-log base 2[(9^x)-6]=1

Please help!!!

Log _{2 }(4.3^{x}-6)- log _{2} (9^{x}-6)=1

Log _{2} ( 4.3^{x}-6)/(9^{x}-6) =1

4.3^{x}-6 = 2 (9^{x}-6)

Put 3^{x} = u

4u -6 = 2( u^{2}-6)

(u^{2}-6)= 2u-3

u^{2}-2u-6+3=0

u^{2} -2u-3=0

u^{2}-3u+u-3=0

u(u-3) +1(u-3) =0

(u-3)(u+1) =0

u =3 or u = -1

3^{x } =3 or 3^{x } = -1

3^{x} = -1 not admissible because of logarithm of negative number

3^{x } =3

x=1

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