Quickly Solve It

$3^{x-2}=81$

$3^{x-2}=3^4$

$\Rightarrow x-2=4$

$x=\boxed{6}$

3^(x-2)=81

log[3^(x-2)]=log(3^4)

(x-2)log3=4log3

x-2=4

x=6

${ 3 }^{ x-2 }=81\\ \frac { { 3 }^{ x } }{ { 3 }^{ 2 } } ={ \left( { 3 }^{ 2 } \right) }^{ 2 }\\ { 3 }^{ x }={ 3 }^{ 6 }\\ \Rightarrow x=6\\$

$3^{x - 2} = 3^4\\ x - 2 = 4\\ x = \color{#69047E}{\boxed{6}}$

3 to the fourth power is equal to 81 so X-2= 4 X-2+2=4+2(balance method) X=2 By the way I am actually 13 and I live in Jamaica My profile is Like that cause I didn't know the age limit so I just set it like this

We know, $3^{4}=81 \text{ so, } 3^{x-2} = 3^{4}$ Taking $log_{3}$ on both sides we get, $x-2=4 \Rightarrow x=\boxed{6}$

we know that 3 by power 4 equals to 81...so x must be 6

3^4=81. x-2=4. x=6 QEDQEDQEDQQEDQEDQEDQEDQEDQED:)