Saket Sharma Solutions for Exercise 1: Exercise 1

What should come in place of question mark $\left(?\right)$ in the following question?

${\left(8\right)}^{2.3}\times {\left(4\right)}^{0.8}\times {\left(16\right)}^{0.4}={\left(2\right)}^{?}$

What is the Value of ${\log }_{10}\left(\cos \mathrm{\theta }\right)+{\log }_{10}\left(\sin \mathrm{\theta }\right)+{\log }_{10}\left(\tan \mathrm{\theta }\right)+{\log }_{10}\left(\cot \mathrm{\theta }\right)+{\log }_{10}\left(\sec \mathrm{\theta }\right)+{\log }_{10}\left(\mathrm{cosec} \mathrm{\theta }\right)$?

Which one of the following is the largest divisor of $3^x+3^{x+1}+3^{x+2}$, if $x$ is any natural number?

If $5^{x+1}-5^{x-1}=600$, then what is the value of ${10}^{2x}$?

What is $\frac{1}{a^{m-n}-1}+\frac{1}{a^{n-m}-1}$ equal to?

If $x=\sqrt{2}, y=\sqrt[3]{3} \text{and} z=\sqrt[6]{6}$, then which one of the following is correct?

${27}^5+3^{13}$ is divisible by

Which of the following is the value of $\mathrm{x}$, if ${\log }_{\mathrm{x}}$$(19\mathrm{x}-30)=3 ?$