# Exponents and Logarithms – Practice questions

Q1. If  ${3}^{x}={5}^{x–1}\phantom{\rule{0ex}{0ex}}$  , find the value of  $a$  if  $x$  can be written as ${\mathrm{log}}_{a}\left(\frac{1}{5}\right)$ .

Q2. Solve for  $x$  : ${e}^{2\mathrm{ln}\left(\mathrm{ln}x\right)}=2–3\mathrm{ln}x–{\left(\mathrm{ln}x\right)}^{2}$ .

Q3. Solve for  $x$  :  ${\mathrm{log}}_{\left(x–2\right)}\left(x–1\right)+1>{\mathrm{log}}_{\left(x–2\right)}6$ .

Q4. Solve for  $x$  :  .

Q5. If  ${\mathrm{log}}_{70}5=a$  ,  ${\mathrm{log}}_{70}7=b$ find the value of    ${\mathrm{log}}_{70}\left(\frac{1}{8}\right)$ in terms of  $a$   and  $b$  .

Q6. Solve for  $x$  :  ${\mathrm{log}}_{9}x={\mathrm{log}}_{3}\left(x–2\right)$  .

Q7. Find the value of  $x$  for which  ${x}^{{\mathrm{log}}_{3}x}>3$  .

Q8. Find the solution of the equation  ${3}^{x}={x}^{3}$  .

Q9. Solve for  $x$  : $\frac{1}{2}\mathrm{log}\left(x+5\right)=\mathrm{log}\left(x–1\right)$ .

Q10. Find the value of  $x$ if: ${\mathrm{log}}_{3}\left(10–{3}^{x}\right)=2–x$ .

Q11. If  , then find the value of  $x$  in the form of  ${a}^{b}$ , where  .