46 views

What is the value of $x$ when $81\times\left (\frac{16}{25} \right )^{x+2}\div\left (\frac{3}{5} \right )^{2x+4}=144?$

1. $1$
2. $-1$
3. $-2$
4. $\text{Can not be determined}$

edited | 46 views
Migrated from GO Civil 2 months ago by Arjun
0
Easiest way is to substitute value,

If you try to smiplify it you may end up something like $(\frac{16}{9})$ $^{x+1}$ = 1 , only -1 stastify

+1 vote
$81\times\left (\frac{16}{25} \right )^{x+2}\div\left (\frac{3}{5} \right )^{2x+4}=144$

$\implies9^{2}\times\left (\frac{16}{25} \right )^{x+2}\div\left (\frac{3}{5} \right )^{2x+4}=144$

$\implies9^{2}\times\left (\frac{4}{5} \right )^{2(x+2)}\div\left (\frac{3}{5} \right )^{2(x+2)}=12^{2}$

$\implies\left [ 9\times\left (\frac{4}{5} \right )^{x+2}\div\left (\frac{3}{5} \right )^{x+2}\right ]^{2}=12^{2}$

$\implies\left [ 9\times\left (\frac{4}{5} \right )^{x+2}\div\left (\frac{3}{5} \right )^{x+2}\right ]=12$

$\implies \left [\left (\frac{4}{5} \right )^{x+2}\div\left (\frac{3}{5} \right )^{x+2}\right ]=\frac{4}{3}$

$\implies\frac{\left(\frac{4}{5}\right)^{x+2}}{\left(\frac{3}{5}\right)^{x+2}} = \frac{4}{3}$

$\implies\left(\frac{4}{3}\right)^{x+2}= \left(\frac{4}{3}\right)^{1}$

Compare both side and we get

$x+2=1$

$\implies x=-1$

So, correct answer is option (B).
by Boss (45.8k points)
selected by

option b is right

by Boss (34.4k points)