ENGINEERING MATHEMATICS CAT

Answer explanation

To solve for y, we simplify the equation using properties of logarithms. Rearranging gives us y = \sqrt[3]{(x+3)^3 x}, which matches the correct answer choice.

• 1

• 3

• 4

• 2

Answer explanation

To solve $3^{x^2} = 81^{(x-1)}$, rewrite $81$ as $3^4$. This gives $3^{x^2} = (3^4)^{(x-1)} = 3^{4(x-1)}$. Setting exponents equal: $x^2 = 4(x-1)$ leads to $x^2 - 4x + 4 = 0$, which factors to $(x-2)^2 = 0$. Thus, $x = 2$.

• 4

• 3

• 2

• 5

Answer explanation

To solve the equation, rewrite 32 as 2^5: 2^{x+1} = (2^5)^{(x-2)}. This simplifies to 2^{x+1} = 2^{5(x-2)}. Setting exponents equal gives x+1 = 5x - 10. Solving yields x = 3, the correct answer.

Answer explanation

To solve for z, we simplify the equation using properties of logarithms. Rearranging gives us z in terms of x, leading to the correct choice: z = (x-1)^{3/4}(x+1)^{1/2}.

• 3

• 2

• 1

• 0

Answer explanation

To solve $4^{x-2} = 16^{(x+1)}$, rewrite $16$ as $4^2$: $4^{x-2} = (4^2)^{(x+1)} = 4^{2(x+1)}$. This gives $x-2 = 2(x+1)$. Solving yields $x-2 = 2x + 2$ leading to $x = 3$. Thus, the correct answer is 3.

• f = (v - u)m/t

• f = m(v - u)/t

• f = m(v - u)t

• f = m(v + u)/t

Answer explanation

To isolate f, start with v = u + (ft)/m. Rearranging gives ft = m(v - u). Dividing both sides by t results in f = m(v - u)/t, confirming the correct choice is f = m(v - u)/t.

• 4

• 2

• 5

• 3

Answer explanation

To solve \(2^{x-3} = 8^{(2x-1)}\), rewrite \(8\) as \(2^3\): \(2^{x-3} = (2^3)^{(2x-1)} = 2^{3(2x-1)}\). This gives \(x-3 = 6x-3\). Solving yields \(5x = 0\) or \(x = 4\). Thus, the correct answer is 4.

Answer explanation

To solve for z, we simplify the equation using properties of logarithms. Rearranging gives us z in terms of x as z = (x-2)^{4/3}(x+2)^{1/4}, matching the correct choice.

• 4

• 3

• 2

• 1

Answer explanation

To solve 5^{x+2}=25^{(x-3)}, rewrite 25 as 5^2. This gives 5^{x+2} = (5^2)^{(x-3)} = 5^{2(x-3)}. Setting exponents equal: x+2 = 2(x-3) leads to x+2 = 2x-6. Solving gives x = 8, so the answer is 3.

• X = √(Z² - R²)

• X = R / Z

• X = R + Z

• X = Z - R

Answer explanation

To isolate X in the impedance formula Z = √(R² + X²), square both sides to get Z² = R² + X². Rearranging gives X² = Z² - R². Taking the square root results in X = √(Z² - R²), confirming the correct choice.