Question

find the vale of x
81x3^x÷3^2x=81​

Answer 1

Answer:

81×3^x÷3^2x=81

3^x=3^2x

x+2x=0

3x=0

x=0

Answer 2

Answer:

x=0

Step-by-step explanation:

$\frac{81 \times {3}^{x} }{ {3}^{2x} } = 81 \\ \frac{ {3}^{4} \times {3}^{x} }{ {3}^{2x} } = {3}^{4} \\ {3}^{4 + x - 2x} = {3}^{4} \\ {3}^{4 - x} = {3}^{4} \\ {3}^{4 - 4} = {3}^{x} \\ {3}^{0} = {3}^{x} \\ 0 = x$

Let's verify :

$\frac{81 \times {3}^{x} }{ {3}^{2x} } = 81 \\ \frac{81 \times {3}^{0} }{ {3}^{2 \times 0} } = 81 \\ \frac{81 \times 1}{ {3}^{0} } = 81 \\ \frac{81 \times 1}{1} = 81 \\ 81 = 81$