5-6-x-3-4-x-2-9-x-I-need-an-explanation-

Question Number 53827 by Mikael_Marshall last updated on 26/Jan/19

5 \times 6^{x} - 3 \times 4^{x} = 2 \times 9^{x}

I n e e d a n e x p l a n a t i o n .

Answered by tanmay.chaudhury50@gmail.com last updated on 26/Jan/19

5 \times 3^{x} \times 2^{x} - 3 \times 2^{x} \times 2^{x} = 2 \times 3^{x} \times 3^{x}

a = 2^{x} b = 3^{x}

5 a b - 3 a^{2} = 2 b^{2}

3 a^{2} - 5 a b + 2 b^{2} = 0

3 a^{2} - 3 a b - 2 a b + 2 b^{2} = 0

3 a (a - b) - 2 b (a - b) = 0

(a - b) (3 a - 2 b) = 0

e i t h e r a - b = 0

a = b

2^{x} = 3^{x}

{(\frac{2}{3})}^{x} = 1 = {(\frac{2}{3})}^{0} s o x = 0

o r w h e n

3 a - 2 b = 0

3 \times 2^{x} = 2 \times 3^{x}

\frac{2^{x}}{3^{x}} = \frac{2}{3}

{(\frac{2}{3})}^{x} = {(\frac{2}{3})}^{1} s o x = 1

h e n c e x i s e i t h e r 0 o r 1

Commented by Mikael_Marshall last updated on 26/Jan/19

t h a n k y o u b r o

Commented by tanmay.chaudhury50@gmail.com last updated on 26/Jan/19

m o s t w e l c o m e \dots