Solving exponential equations using exponent rules

Lessons

• 1.
  Solve for "$x$", with common base
  a)

  $2^x=2^5$
  
  
  b)

  $3^{2x+1}=3^{11}$
  
  

---

• 2.
  Solve for "$x$", by converting to common base
  a)

  $3^{4x-8}=27^{-2x}$
  
  
  b)

  $8^{7-2x}=16^{5x+10}$
  
  
  c)

  $3^{\frac{x}{4}-\frac{4}{5}}=81{^5}\sqrt{729}$
  
  
  d)

  $\frac{1}{81^{2-x}}=27^{4x+5}$
  
  
  e)

  $(\frac{1}{4})^{1-2x}=8^{x-3}$
  
  
  f)

  $9^{x+2}=(3^{4x-3})(3^5)$
  
  
  g)

  $(\frac{343}{1000})^{-\frac{12}{x}}=(\frac{10}{7})^x$
  
  

---

• 3.
  Solve: $5(9^x)+40(3^x)-45=0$

---