Solve the following equation for x ($\frac{5}{6}$)^{x + 1} = ($\frac{216}{125}$)^{2x + 3}

Solve the following equation for x without using tables or calculators

($\frac{5}{6}$)^{x + 1} = ($\frac{216}{125}$)^{2x + 3}

Answers

($\frac{5}{6}$)^{x + 1} = ($\frac{216}{125}$)^{2x + 3}

this is the same as

($\frac{5}{6}$)^{x + 1} = ($\frac{125}{216}$)^{-2x - 3}; ($\frac{5}{6}$)^{x + 1} = ($\frac{5^3}{6^3}$)^{-2x - 3}

($\frac{5}{6}$)^{x + 1} = ($\frac{5}{6}$)^{-3(2x + 3)}

x + 1 = -6x - 9

7x = - 10; x = -$\frac{10}{7}$

---

johnmulu answered the question on March 6, 2017 at 07:12

Next: The largest angle of a triangle exceeds ten times the smallest angle by 10^o. The third angle is equal by 60^o. Find the size of the largest angle.
Previous: Simplify $\frac{2x^2 – 3xy – 2y^2}{4x^2 – y^2}$

View More Mathematics Questions and Answers | Return to Questions Index

Exams With Marking Schemes

• Grade 1
• Grade 2
• Grade 3
• Grade 4
• Grade 5
• Grade 6
• Grade 7
• Grade 8
• Grade 9
• PP1
• PP2
• Playgroup
• Form 1
• Form 2
• Form 3
• Form 4

Related Questions

• The largest angle of a triangle exceeds ten times the smallest angle by 10^o. The third angle is equal by 60^o. Find the size of the largest angle.(Solved)
  

  The largest angle of a triangle exceeds ten times the smallest angle by 10^o. The third angle is equal by 60^o. Find the size of the largest angle.

  Date posted: March 6, 2017.  Answers (1)

• Two farm workers Mutua and Musyoka can cultivate a field in 6 days. Mutua alone can complete the cultivation in 15 days. After Mutua and Musyoka had worked for 4 days, Mutua fell sick(Solved)
  

  Two farm workers Mutua and Musyoka can cultivate a field in 6 days. Mutua alone can complete the cultivation in 15 days. After Mutua and Musyoka had worked for 4 days, Mutua fell sick. Find the time taken by Musyoka to complete the cultivation.

  Date posted: March 6, 2017.  Answers (1)

• Evaluate$\frac{14\div \frac{1}{3} of\; 5\frac{1}{4} - \;\frac{3}{4}\times\;1 \frac{1}{3}}{\frac{3}{5}\times 6\frac{1}{4} + 1\frac{1}{2}}$(Solved)
  

  Without using a calculator evaluate
  
  $\frac{14\div \frac{1}{3} of\; 5\frac{1}{4} - \;\frac{3}{4}\times\; 1\frac{1}{3}}{\frac{3}{5}\times 6\frac{1}{4} + 1\frac{1}{2}}$

  Date posted: March 6, 2017.  Answers (1)

• A garage owner bought a certain number of litres of petrol for sh 760. If the petrol cost sh x per litre........(Solved)
  

  A garage owner bought a certain number of litres of petrol for sh 760. If the petrol cost sh x per litre
  a) write down an expression for the number of litres of petrol he obtained
  b) When the price per litre was up by 25 cents he found that he obtained 5 litres fewer for the same sum of money
  i) Form an equation in x and show that it reduces to 4x² + x – 95 = 0
  ii) Solve the equation and calculate the price of petrol after the rise
  

  Date posted: March 6, 2017.  Answers (1)

• In harambee organized in aid of a school development project, it was decided that each , man present would pay sh 200 and each woman sh 150. There were altogether 400 men and women present. If the harambee raised sh 69 200 in this way(Solved)
  

  In harambee organized in aid of a school development project, it was decided that each , man present would pay sh 200 and each woman sh 150. There were altogether 400 men and women present. If the harambee raised sh 69 200 in this way, Find the number of men present

  Date posted: March 6, 2017.  Answers (1)

• Two grades of coffee A and grade B costing sh 30 per kg and sh 24 to produce a mixture costing sh 26.40 per kg. Determine the ratio in which grade A and B were mixed (Solved)
  

  Two grades of coffee A and grade B costing sh 30 per kg and sh 24 to produce a mixture costing sh 26.40 per kg. Determine the ratio in which grade A and B were mixed

  Date posted: March 6, 2017.  Answers (1)

• Use tables of square roots and squares to evaluate to 4 significant figures 4.346² + $\sqrt{47.32}$(Solved)
  

  Use tables of square roots and squares to evaluate to 4 significant figures
  
  4.346² + $\sqrt{47.32}$

  Date posted: March 6, 2017.  Answers (1)

• The lines 3x + 2y – 7 = 0 and ax + 3y + 2 = 0 Are perpendicular(Solved)
  

  The lines 3x + 2y – 7 = 0 and ax + 3y + 2 = 0
  Are perpendicular
  

  Date posted: March 6, 2017.  Answers (1)

• Simplify the expression: 4x - $\frac{3x + y}{8}$ - $\frac{x – 3y}{4}$ (Solved)
  

  Simplify the expression:
  4x - $\frac{3x + y}{8}$ - $\frac{x – 3y}{4}$
  

  Date posted: March 6, 2017.  Answers (1)

• The numerator of a fraction is three less than the denominator. When both the numerator and the denominator are increased by 5, the fraction becomes $\frac{5}{6}$. Find the original fraction(Solved)
  

  The numerator of a fraction is three less than the denominator. When both the numerator and the denominator are increased by 5, the fraction becomes $\frac{5}{6}$. Find the original fraction

  Date posted: March 6, 2017.  Answers (1)

• Evaluate $\frac{200\div 4 – (40 - 54)}{-72\div 6 + 20\; of\; 6 – 9\times 4}$(Solved)
  

  Evaluate
  $\frac{200\div 4 – (40 - 54)}{-72\div 6 + 20\; of\; 6 – 9\times 4}$

  Date posted: March 6, 2017.  Answers (1)

• A number between 200 and 300 has its tens digit four more than the units digit. If the number is written in the reverse order the number increases by 99. Find the number.(Solved)
  

  A number between 200 and 300 has its tens digit four more than the units digit. If the number is written in the reverse order the number increases by 99. Find the number.

  Date posted: March 6, 2017.  Answers (1)

• Solve $\frac{7x + 1}{9}$ - $\frac{3x - 1}{7}$ = 2(Solved)
  

  Solve $\frac{7x + 1}{9}$ - $\frac{3x - 1}{7}$ = 2

  Date posted: March 6, 2017.  Answers (1)

• Find the sum of all the prime numbers between 1 and 10.(Solved)
  

  Find the sum of all the prime numbers between 1 and 10.

  Date posted: March 6, 2017.  Answers (1)

• Find the equation of a straight line which passes through the point of intersection of lines x – 3y = 4 and 3x + y = 2 (Solved)
  

  Find the equation of a straight line which passes through the point of intersection of lines x – 3y = 4 and 3x + y = 2 and is parallel to the line 3x + 4y = 0

  Date posted: March 6, 2017.  Answers (1)

• Given that a = 2, b = 1 and c = 3, find the value of(Solved)
  

  Given that a = 2, b = 1 and c = 3, find the value of
  
  $\frac{3a^2 - 2b^2 + 4b}{2ac + 2b^3 - 3c}$

  Date posted: March 2, 2017.  Answers (1)

• If log2 = 0.3010, log3 = 0.4771 and log 5 = 0.6990, Find the logarithm of 3.3 (Solved)
  

  If log2 = 0.3010, log3 = 0.4771 and log 5 = 0.6990, Find the logarithm of 3.3

  Date posted: March 2, 2017.  Answers (1)

• A woman went on a journey by walking,by bus and by matatu. She went by bus for $\frac{4}{5}$ of the distance, then by matatu $\frac{2}{3}$ of the rest of the distance, then walked the remaining distance(Solved)
  

  A woman went on a journey by walking,by bus and by matatu. She went by bus for $\frac{4}{5}$ of the distance, then by matatu $\frac{2}{3}$ of the rest of the distance, then walked the remaining distance. The distance travelled by the bus was 55 km more than the distance walked. Find the total distance

  Date posted: March 2, 2017.  Answers (1)

• Without using tables, find the value of $\frac{P}{Q}$ when P = 1.44 x 10^-6(Solved)
  

  Without using tables, find the value of $\frac{P}{Q}$ when P = 1.44 x 10^-6 and Q = 4.8 x 10^-4 giving your answers in the form A x 10ⁿ where A is A number between 1 to 10 and n is an integer.

  Date posted: March 2, 2017.  Answers (1)

• Find the L.C.M. of x² - xy - 12y² and x - 4y, Hence simplify(Solved)
  

  Find the L.C.M. of x² - xy - 12y² and x - 4y, Hence simplify
  
  $\frac{7}{x^2 - xy + 12y^2}$ - $\frac{1}{x - 4y}$

  Date posted: March 2, 2017.  Answers (1)