Embibe Experts Solutions for Exercise 7: Assignment

Number of solutions of inequation $\left|2^x-1\right|+\left|4-2^x\right|<3$ are ______.

Let $f\left(x\right)=\sqrt{x^2+2x+1}-\sqrt{x^2-2x+1}$ then value of $f\left(\frac{-5}{4}\right)+f\left(\frac{3}{4}\right)+f\left(\frac{7}{4}\right)$ is equal to ______.

The value of ${81}^{\frac{1}{{\log }_{5}3}}+{27}^{{\log }_{9}36}+3^{\frac{4}{{\log }_{7}9}}$ is equal to ______.

If ${\log }_{\left(x+3\right)}\left(x^2-x\right)<1$ is satisfied for $x\in \left(a,b\right)\cup \left(c,d\right)\cup \left(e,f\right)$ then value of $\left|a+b+c+d+e+f\right|+1$ is equal to _____.

The product of roots of the equation $\frac{{\log }_8\left({\displaystyle \frac{8}{x^2}}\right)}{{\left({\log }_{8}x\right)}^2}=3$ is equal to ______.

If $\alpha$ and $\beta$ are the roots of the equation $e^2{x}^{\ln x}=x^3$ with $\alpha >\beta$ such that ${\alpha }^m={\beta }^n$ is true (where $m,n$ are coprime to each other) then value of $m\times n$ is equal to __

If $m={\log }_{245}175$ and $n={\log }_{1715}875$ then the value of $\frac{m-n}{1-mn}$ is equal to ______.

The unique value of $x$ satisfying the equation $4^x-3^{x-\frac{1}{2}}=3^{x+\frac{1}{2}}-2^{2x-1}$ is equal to _____