Solve the equation;

      

Solve the equation;
Log (x²-8x+20) = Log 4 + Log (x-4)

  

Answers

---

Log (x² – 8x = 20) = log 4 (x-4)
x² – 8x +20 = 4x – 16
x² -8x -4x + 20 + 16 = 0
x² – 12x + 36 = 0
x² – 6x – 6x + 36 = 0
x(x-6) -6(x-6) = 0
(x-6) (x-6) = 0
x = 6

---

Kavungya answered the question on September 20, 2019 at 06:11

Next: Find the matrix of transformation that would map triangle ABC with vertices at A(-5,2), B(-3,2) and C(-3,5) onto triangle A¹B¹C¹ with vertices at A¹(-5,-2), B¹(-3,-2)...
Previous: Equal masses of magnesium ribbon were reacted separately with equal volumes of 1M hydrochloric acid and 1M methanoic acid. The results were plotted on a...

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

---

• Find the matrix of transformation that would map triangle ABC with vertices at A(-5,2), B(-3,2) and C(-3,5) onto triangle A¹B¹C¹ with vertices at A¹(-5,-2), B¹(-3,-2)...(Solved)
  

  Find the matrix of transformation that would map triangle ABC with vertices at A(-5,2), B(-3,2) and
  C(-3,5) onto triangle A¹B¹C¹ with vertices at A¹(-5,-2), B¹(-3,-2) and C¹(-3,-5).
  

  Date posted: September 20, 2019.  Answers (1)

• Rationalize the following leaving your answer in the simplified surd form.(Solved)
  

  Rationalize the following leaving your answer in the simplified surd form.
  

  Date posted: September 20, 2019.  Answers (1)

• If ? is an acute angle find the value of Cos ? in the panating: 4 Sin²?-5 Cos ?+2=0(Solved)
  

  If θ is an acute angle find the value of Cos θ in the panating:
  4 Sin²θ-5 Cos θ+2=0

  Date posted: September 20, 2019.  Answers (1)

• Give that x= 4 is a root of x²+kx-20=0. Find the value of k and thus other roots(Solved)
  

  Give that x= 4 is a root of x²+kx-20=0. Find the value of k and thus other roots

  Date posted: September 20, 2019.  Answers (1)

• Copy and complete the table below for the function y=4+5x-x² for -2=x=7(Solved)
  

  Copy and complete the table below for the function y=4+5x-x² for -2≤x≤7
  

  Date posted: September 20, 2019.  Answers (1)

• A supermarket is stocked with plates which come from two suppliers A and B. They are bought in the ratio of 3:5 respectively, 10% of...(Solved)
  

  A supermarket is stocked with plates which come from two suppliers A and B. They are bought in the ratio of 3:5 respectively, 10% of plates from A are defective and 6% of the plates from B are defective.
  (a) A plate is chosen by a buyer at random. Find the probability that;
  (i) it is from A
  (ii) it is from B and it is defective.
  (iii) it is defective
  (b) Two plates are chosen at random. Find the probability that:
  (i) both are defective
  (ii) at least one is not defective.

  Date posted: September 20, 2019.  Answers (1)

• The points X and Y are both on latitude 39^oN. The longitude of X is 73^oW and the longitude of Y is 18^oW . Two...(Solved)
  

  The points X and Y are both on latitude 39^oN. The longitude of X is 73^oW and the longitude of Y is 18^oW . Two ships P and Q leave X at the same time and travel to Y along the line of latitude. The ships P and Q travel at constant speeds of 25km/hr and 20km/h respectively. Taking the radius of the earth to be 6371km and π= 22/7 ;Calculate:-
  (a) The distance Q still has to travel when P reaches Y.
  (b) At the same time a third ship R leaves Y traveling due west at an average speed of 15km/hr.
  Calculate the longitude of the point at which R meets P.
  

  Date posted: September 20, 2019.  Answers (1)

• In a square PQRS, A is the mid-point of PQ and B is the mid-point of QR, while C is a point on BP such...(Solved)
  

  In a square PQRS, A is the mid-point of PQ and B is the mid-point of QR, while C is a point on BP such that 2BC = 3CP. The co-ordinates of P, Q and S are (4,4), (14,4) and (4,14) respectively. Find:
  (a) (i) the column vectors of PQ and PS.
  (ii) co-ordinates of R
  (b) Show that A, C, S are collinear.

  Date posted: September 20, 2019.  Answers (1)

• The n^th term of a series is given by 3n+4. (a) Write down the first four terms of the series. (b) Find the sum of the first...(Solved)
  

  The n^th term of a series is given by 3n+4.
  (a) Write down the first four terms of the series.
  (b) Find the sum of the first twenty terms of the series.
  (c) Find the 30^th term.
  (d) Show that the sum of the first n terms of the sequence is given by S_n=3/2n²+11/2n. Hence or otherwise, find the largest integral value of n such that Sn ≥130.

  Date posted: September 20, 2019.  Answers (1)

• Find the equation of the tangent to the circle x²+y²-8x+2y+7=0 at the point (3, 2). Give your answer in the form y=ax+b. (Solved)
  

  Find the equation of the tangent to the circle x²+y²-8x+2y+7=0 at the point (3, 2). Give your answer in the form y=ax+b.

  Date posted: September 19, 2019.  Answers (1)

• Without using mathematical tables and calculators simplify:(Solved)
  

  Without using mathematical tables and calculators simplify:
  

  Date posted: September 19, 2019.  Answers (1)

• In the figure below, AB is a tangent, meeting chord CDE at B. DE=xcm Determine: (a) the value of x (b) the length of AB (Solved)
  

  In the figure below, AB is a tangent, meeting chord CDE at B. DE=xcm
  
  Determine:
  (a) the value of x
  (b) the length of AB

  Date posted: September 19, 2019.  Answers (1)

• PQRS is a cyclic quadrilateral in which PQ=6cm, QR=2cm, RS=6.5cm, PR=7.2cm and angle PRS=70^o. Determine values of x.(Solved)
  

  PQRS is a cyclic quadrilateral in which PQ=6cm, QR=2cm, RS=6.5cm, PR=7.2cm and angle PRS=70^o.
  
  Determine values of x.

  Date posted: September 19, 2019.  Answers (1)

• Use matrix method to solve simultaneous equations. 3x + 7y = 11 x – y + 4 = 0 (Solved)
  

  Use matrix method to solve simultaneous equations.
  3x + 7y = 11
  x – y + 4 = 0
  

  Date posted: September 19, 2019.  Answers (1)

• The distance between Sotik and Nakuru is 130km. car x starts from Sotik at 8.00 a.m and travels at 40km/hr towards Nakuru. A second car...(Solved)
  

  The distance between Sotik and Nakuru is 130km. car x starts from Sotik at 8.00 a.m and travels at 40km/hr towards Nakuru. A second car y starts traveling from Nakuru at 8.15 a.m towards Sotik at an average speed of 35km/hr. At what time will the two cars meet?

  Date posted: September 19, 2019.  Answers (1)

• A variable P varies as the square of Q and inversely as square root of R. Find the percentage change in P when Q is...(Solved)
  

  A variable P varies as the square of Q and inversely as square root of R. Find the percentage change in P when Q is increased by 5% and R reduced by 19%.

  Date posted: September 19, 2019.  Answers (1)

• Make C the subject of the formula.(Solved)
  

  Make C the subject of the formula.
  

  Date posted: September 19, 2019.  Answers (1)

• (a) Expand and simplify the expression (10+2/x)⁵ (b) Use the expression in (a) above to find the value of 14⁵. (Solved)
  

  (a) Expand and simplify the expression (10+2/x)⁵
  (b) Use the expression in (a) above to find the value of 14⁵.
  

  Date posted: September 19, 2019.  Answers (1)

• The table below is part of tax table for monthly income for the year 2010. Monthly taxable income in Ksh. Tax rate % in...(Solved)
  

  The table below is part of tax table for monthly income for the year 2010.
  Monthly taxable income in Ksh. Tax rate % in each sh.
  Under Ksh. 9681 10%
  From Ksh. 9681 but under 18801 15%
  From Ksh. 18801 but under Kshs.27921 20%
  In the year 2010, the tax on Koech’s monthly income was Ksh.1916. Calculate Koech’s monthly income.

  Date posted: September 19, 2019.  Answers (1)

• Evaluate:(Solved)
  

  Evaluate:
  

  Date posted: September 19, 2019.  Answers (1)