algebra

If a positive real x satisfies the following equation log₂ x + log√₂ x = 48, then the value of x is

The real variables x, y, z, and the real constants p, q, r satisfy $\frac{x}{pq - r^2} = \frac{y}{qr - p^2} = \frac{z}{rp - q^2}$ Given that the denominators are non-zero, the valu...

The real variables $x, y, z$, and the real constants $p, q, r$ satisfy $\frac{x}{pq - r^2} = \frac{y}{qr - p^2} = \frac{z}{rp - q^2}$ Given that the denominators are non-zero, the...

Consider the following inequalities p² - 4q < 4 3p + 2q < 6 where p and q are positive integers. The value of (p + q) is _________.

Consider the following inequalities 𝑝 2 − 4𝑞 < 4 3𝑝 + 2𝑞 < 6 where 𝑝 and 𝑞 are positive integers. The value of (𝑝 + 𝑞) is _______.

Which one of the following is a representation (not to scale and in bold) of all values of x satisfying the inequality $2-5x\leq-\left(\frac{6x-5}{3}\right)\;$ on the real number l...

If ⊕ ÷ ⊙ = 2; ⊙ ÷ Δ = 3; ⊙ + Δ = 5; Δ × ⊗ = 10, Then, the value of (⊗ − ⊕)², is:

The sum and product of two integers are 26 and 165 respectively. The difference between these two integers is ________.

The sum and product of two integers are 26 and 165 respectively. The difference between these two integers is ____.

A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m² of area. What is the area of the...

The value of the expression $\frac{1}{1+\log_u vw} + \frac{1}{1+\log_v wu} + \frac{1}{1+\log_w uv}$ is

A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?

A rectangle becomes a square when its length and breadth are reduced by 10 m and 5 m, respectively. During this process, the rectangle loses 650 m 2 of area. What is the area of th...

A number consists of two digits. The sum of the digits is 9. If 45 is subtracted from the number, its digits are interchanged. What is the number?

For integers a, b and c, what would be the minimum and maximum values respectively of a + b + c if log |a| + log |b| + log |c| = 0?

The value of the expression $${1 \over {1 + \log _u^{vw}}} + {1 \over {1 + \log _v^{wu}}} + {1 \over {1 + \log _w^{uv}}}$$ is

If $$\,\,\,y = x + \sqrt {x + \sqrt {x + \sqrt {x + .....\alpha } } } \,\,\,$$ then $$y(2)=$$ __________.