Solve logarithmic equation

Algebra
Tutor: None Selected Time limit: 1 Day

Instructions: find x

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

Please help!!!

Dec 9th, 2014

Log 2 (4.3x-6)- log 2 (9x-6)=1

Log 2 ( 4.3x-6)/(9x-6) =1

4.3x-6 = 2 (9x-6)

Put 3x = u

4u -6 = 2( u2-6)

(u2-6)= 2u-3

u2-2u-6+3=0

u2 -2u-3=0

u2-3u+u-3=0

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

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

u =3 or u = -1

3x  =3 or 3x  = -1

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

3x  =3

x=1


Dec 9th, 2014

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