Solve for \( x \) a) \( 5^{x}=25 \) d) \( 2^{8}=4^{x} \) g) \( \frac{1}{2^{x}}=8 \) j) \( -2^{x}=-32 \) m) \( 5^{-2}=\frac{1}{25^{x}} \) p) \( 3^{x-2}=\frac{1}{3^{x}} \) s) \( 10^{x}=1 \) v) \( 27^{x-2}=81^{2 x+1} \)

Solve the equation by following steps: - step0: Solve for \(x\): \(-2^{x}=-32\) - step1: Change the signs: \(2^{x}=32\) - step2: Rewrite in exponential form: \(2^{x}=2^{5}\) - step3: Set the exponents equal: \(x=5\) Solve the equation \( 2^{8}=4^{x} \). Solve the equation by following steps: - step0: Solve for \(x\): \(2^{8}=4^{x}\) - step1: Swap the sides: \(4^{x}=2^{8}\) - step2: Rewrite in exponential form: \(2^{2x}=2^{8}\) - step3: Set the exponents equal: \(2x=8\) - step4: Divide both sides: \(\frac{2x}{2}=\frac{8}{2}\) - step5: Divide the numbers: \(x=4\) Solve the equation \( 27^{x-2}=81^{2 x+1} \). Solve the equation by following steps: - step0: Solve for \(x\): \(27^{x-2}=81^{2x+1}\) - step1: Rewrite the expression: \(3^{3x-6}=3^{8x+4}\) - step2: Set the exponents equal: \(3x-6=8x+4\) - step3: Move the expression to the left side: \(3x-8x=4+6\) - step4: Add and subtract: \(-5x=4+6\) - step5: Add and subtract: \(-5x=10\) - step6: Change the signs: \(5x=-10\) - step7: Divide both sides: \(\frac{5x}{5}=\frac{-10}{5}\) - step8: Divide the numbers: \(x=-2\) Solve the equation \( \frac{1}{2^{x}}=8 \). Solve the equation by following steps: - step0: Solve for \(x\): \(\frac{1}{2^{x}}=8\) - step1: Rearrange the terms: \(2^{-x}=8\) - step2: Rewrite in exponential form: \(2^{-x}=2^{3}\) - step3: Set the exponents equal: \(-x=3\) - step4: Change the signs: \(x=-3\) Solve the equation \( 5^{x}=25 \). Solve the equation by following steps: - step0: Solve for \(x\): \(5^{x}=25\) - step1: Rewrite in exponential form: \(5^{x}=5^{2}\) - step2: Set the exponents equal: \(x=2\) Solve the equation \( 3^{x-2}=\frac{1}{3^{x}} \). Solve the equation by following steps: - step0: Solve for \(x\): \(3^{x-2}=\frac{1}{3^{x}}\) - step1: Rewrite the expression: \(3^{x-2}=3^{-x}\) - step2: Set the exponents equal: \(x-2=-x\) - step3: Move the variable to the left side: \(x-2+x=0\) - step4: Add the terms: \(2x-2=0\) - step5: Move the constant to the right side: \(2x=0+2\) - step6: Remove 0: \(2x=2\) - step7: Divide both sides: \(\frac{2x}{2}=\frac{2}{2}\) - step8: Divide the numbers: \(x=1\) Solve the equation \( 10^{x}=1 \). Solve the equation by following steps: - step0: Solve for \(x\): \(10^{x}=1\) - step1: Rewrite in exponential form: \(10^{x}=10^{0}\) - step2: Set the exponents equal: \(x=0\) Solve the equation \( 5^{-2}=\frac{1}{25^{x}} \). Solve the equation by following steps: - step0: Solve for \(x\): \(5^{-2}=\frac{1}{25^{x}}\) - step1: Rearrange the terms: \(5^{-2}=25^{-x}\) - step2: Swap the sides: \(25^{-x}=5^{-2}\) - step3: Rewrite in exponential form: \(5^{-2x}=5^{-2}\) - step4: Set the exponents equal: \(-2x=-2\) - step5: Change the signs: \(2x=2\) - step6: Divide both sides: \(\frac{2x}{2}=\frac{2}{2}\) - step7: Divide the numbers: \(x=1\) Here are the solutions for each equation: a) \( 5^{x} = 25 \) - Solution: \( x = 2 \) d) \( 2^{8} = 4^{x} \) - Solution: \( x = 4 \) g) \( \frac{1}{2^{x}} = 8 \) - Solution: \( x = -3 \) j) \( -2^{x} = -32 \) - Solution: \( x = 5 \) m) \( 5^{-2} = \frac{1}{25^{x}} \) - Solution: \( x = 1 \) p) \( 3^{x-2} = \frac{1}{3^{x}} \) - Solution: \( x = 1 \) s) \( 10^{x} = 1 \) - Solution: \( x = 0 \) v) \( 27^{x-2} = 81^{2x+1} \) - Solution: \( x = -2 \) If you have any further questions or need additional assistance, feel free to ask!