Maharashtra Board Solutions for Chapter: Functions, Exercise 3: MISCELLANEOUS EXERCISE

If ${\log }_{10}\frac{28}{45}-{\log }_{10}\frac{35}{324}+{\log }_{10}\frac{325}{432}-{\log }_{10}\frac{13}{15}={\log }_{10}k$, then find the value of $k$.

Solve for $x,{\log }_x(8x-3)-{\log }_{x}4=2.$

Solve $\sqrt{{\log }_2{x}^4}+4{\log }_4\sqrt{\frac{2}{x}}=2$.

Find value of $\frac{3+{\log }_{10}343}{2+\frac{1}{2}{\log }_{10}\left(\frac{49}{4}\right)+\frac{1}{2}{\log }_{10}\left(\frac{1}{25}\right)}$.

If $\frac{{\log }_{2}a}{4}=\frac{{\log }_{2}b}{6}=\frac{{\log }_{2}c}{3k}\text{ and }{a}^3{b}^{2}c=1$ Find the value of $k.$

Solve the following for $x,$ where $\left|x\right|$ is modulus function, $\left[x\right]$ is greatest integer function, $\left\{x\right\}$ is a fractional part function.

$[x-2]+[x+2]+\left\{x\right\}=0$

Find $k$ if $f\left(x\right)=x^2+k$, where $g\left(x\right)=1+\sqrt{x}\text{ and }f\left[g\right(x\left)\right]=3+2\sqrt{x}+x$.

Find $(f\circ f)\left(x\right)$ if $f\left(x\right)=\frac{2x+1}{3x-2}$.