Basic of Mathematics

If $x^{\log } 7^x \gt 7$ where $x \gt 0$, then which one of the following is correct?

What is the minimum value of $|x|$ ?

What is the solution of $x \leq 4, y^3 0$ and $x \leq-4, y \leq 0$ ?

If $\left.A=\mid x \in R: x^2+6 x-7 \lt 0\right\}$ and $B=\left\{x \in R: x^2+9 x+14 \gt 0\right\}$, then which of the following is/ are correct? $(A \cap B)=(-2,1)$ $(A / B)=(-7,-2)$ Select the correct answer using the…

Let $\mathrm{A} \cup \mathrm{B}=\{x \mid(x-a)(x-b) \gt 0$, where $a \lt b\}$. What are $A$ and $B$ equal to?

If $\log x a, a x$ and $\log b x$ are in G.P, then what is $x$ equal to?

If $1!+3!+5!+7!+\ldots+199$ ! is divided by 24 , what is the remainder?

If $x y=4225$ where $x, y$ are natural numbers, then what is the minimum value of $x+y$ ?

For the following two (02) items: Let $p = \sum_{j=1}^{n} \log_{10} 2^j$ and $q = \sum_{j=1}^{n} \log_{10} 5^j$. If $p + q = 15$, then what is $q - p$ equal to?

For $x \geq y \gt 1$, let $\log _x\left(\frac{x}{y}\right)+\log _y\left(\frac{y}{x}\right)=k$, then the value of $k$ can never be equal to:

If $\log _{10} 2 \log _2 10+\log _{10}\left(10^x\right)=2$, then what is the value of $x$ ?

What is the number of solutions of $\log _4(x-1)=$ $\log _2(x-3)$ ?