21. What value of $x$ makes the equation $-\frac{1}{81}=-3^{x}$ true?

Step 1 ：Rewrite the equation in exponential form: \( -\frac{1}{81} = (-3)^x \)

Step 2 ：Take the reciprocal of both sides: \( -\frac{1}{81} = \frac{1}{(-3)^x} \)

Step 3 ：Rewrite \((-3)^x\) as \(\frac{1}{3^x}\): \( -\frac{1}{81} = \frac{1}{3^x} \)

Step 4 ：Multiply both sides by 81: \( -1 = 81 \cdot \frac{1}{3^x} \)

Step 5 ：Simplify the right side: \( -1 = \frac{81}{3^x} \)

Step 6 ：Rewrite 81 as \(3^4\): \( -1 = \frac{3^4}{3^x} \)

Step 7 ：Apply the quotient rule of exponents: \( -1 = 3^{4-x} \)

Step 8 ：Since the bases are the same, the exponents must be equal: \( 4-x = 0 \)

Step 9 ：Solve for \(x\): \( x = 4 \)