Question

Solve for x
729^ x-2=81^x+2

Answer 1

${729}^{x - 2} = {81}^{x + 2}$

Prime Factor of

729=3×3×3×3×3×3

81=3×3×3×3

Means

729=3^6

81=3^4

Now it can be Written as

$( {3}^{6} ) {}^{x - 2} = ({3}^{4} ) {}^{x + 2}$

According to Law of Exponent

If (a^x)^y=a^xy

Means Both power will be multiplied

${3}^{6(x - 2)} = {3}^{4(x + 2)} \\ \\ {3}^{6x - 12} = {3}^{4x + 8}$

Now According to Law of Exponent if

a^x=a^y

x=y

So,

now Power Will be written as equal

${3}^{6x - 12} = {3}^{4x + 8} \\ \\ 6x - 12 = 4x + 8 \\ \\ 6x - 4x = 8 + 12 \\ \\ 2x = 20 \\ \\ x = \frac{20}{2} \\ \\ x = 10$

$\underline{\underline{\mathbf{\huge{X=10}}}}$