Sue Pemberton, Julianne Hughes and, Julian Gilbey Solutions for Chapter: Logarithmic and Exponential Functions, Exercise 2: EXERCISE 2A

Without using a calculator, find the value of ${\log }_{10}100$.

Without using a calculator, find the value of ${\log }_{10}0.0001$.

Without using a calculator, find the value of ${\log }_{10}\left(10\sqrt{10}\right)$.

Without using a calculator, find the value of ${\log }_{10}\left(\sqrt[3]{10}\right)$.

Write the answer with three decimal places only.

Without using a calculator, find the value of ${\log }_{10}\left(100\sqrt[3]{10}\right)$.

Write the answer with three decimal places only.

Without using a calculator, find the value of ${\log }_{10}\left(\frac{100}{\sqrt{1000}}\right)$.

 Given that the function $f$ is defined as $f:x\mapsto {10}^x-3$ for $x\in R$, find an expression for $f^{-1}\left(x\right)$.

Given that $p$ and $q$ are positive and that $4{\left({\log }_{10}p\right)}^2+2{\left({\log }_{10}q\right)}^2=9$, find the greatest possible value of $p$.