Question

(3/2)^6×(4/9)^5=(2/3)^x+2. find x.

hi friends !!!!
can someone please help me by answering the question with all the steps?

Answer 1

Hi ,

( 3/2 )^6 × ( 4/9 )^5 = ( 2/3 )^x+2

( 3/2 )^6 ×[ ( 2/3 )² ]^5 = ( 2/3 )^x+ 2

( 3/2 )^6 × ( 2/3 )^10 = ( 2/3 )^x+2

[since ( a^m )^n = a^mn ]


( 2/3 )^-6 × ( 2/3 )^10 = ( 2/3 )^x+2

[ since ( a/b )^n = ( b/a )^-n ]

( 2/3 )^-6+10 = ( 2/3 )^x+2

[ since a^m × a^n = a^m+n ]

( 2/3 )⁴ = ( 2/3 )^x+2

4 = x + 2

[ If a^m = a^n then m = n ]

4 - 2 = x

2 = x

Therefore ,

x = 2

I hope this helps you.

: )

Answer 2

Given : (3/2)^6 * (4/9)^5 = (2/3)^x+2

$( \frac{3}{2})^6 * ( \frac{4}{9} )^5 = ( \frac{2}{3}) ^{x+2}$

=> $\frac{3^6 * 4^5}{2^6 * 9^5} = ( \frac{2}{3}) ^{x+2}$

$= \ \textgreater \ \frac{ 2^{10} * 3^6}{2^6 * 3^{10} } = ( \frac{2}{3} )^{x+2}$

$= \ \textgreater \ (\frac{2}{3} )^4 = ( \frac{2}{3} )^{x+2}$

= > 4 = x + 2

= > 4 - 2 = x

= > x = 2.


Hope this helps!