The roots of the equation 2x+2 ⋅ 3(3 x/x-1)=9 are given by

Question

The roots of the equation 2x+2 ⋅ 3(3 x/x-1)=9 are given by (A)  log 2,((2/3))-2 (B) 3,-3 (C) -2,1-( log 3/ log 2) (D) 1- log 2 3,2

Tardigrade Admin · Accepted Answer

We have, 2x+2 ⋅ 33 x /(x-1)=9=32 ⇒ (x+2) log 2+(3 x/x-1) log 3 =2 log 3 ⇒ (x+2) log 2+((3 x/x-1)-2) log 3=0 ⇒ (x+2)( log 2+(1/x-1) log 3)=0 ⇒ x=-2 or x=1-( log 3/ log 2) .

Q. The roots of the equation $2^{x + 2} \cdot 3^{\frac{3 x}{x - 1}} = 9$ are given by

$lo g_{2}, (\frac{2}{3}) - 2$

$3, - 3$

$- 2, 1 - \frac{l o g 3}{l o g 2}$

$1 - lo g_{2} 3, 2$

Q. The roots of the equation 2x+2⋅3x−13x​=9 are given by

log2​,(32​)−2

3,−3

−2,1−log2log3​

1−log2​3,2

We have, 2x+2⋅33x/(x−1)=9=32 ⇒(x+2)log2+x−13x​log3=2log3 ⇒(x+2)log2+(x−13x​−2)log3=0 ⇒(x+2)(log2+x−11​log3)=0 ⇒x=−2 or x=1−log2log3​.

Q. The roots of the equation $2^{x + 2} \cdot 3^{\frac{3 x}{x - 1}} = 9$ are given by

$lo g_{2}, (\frac{2}{3}) - 2$

$3, - 3$

$- 2, 1 - \frac{l o g 3}{l o g 2}$

$1 - lo g_{2} 3, 2$