LOG 2

If log₉(32x + 17)=2; find x.

   Solution

Log₉(32x + 17)=2

(32x + 17)=9²       

                                            

32x + 17=81

32x =81 – 17

32x = 64

32x =   64   

32        32

x = 2

Hence x = 2

TRY THIS………………

If log₇(2t - 65)=2; find t

VARIATIONS 1

x is inversely proportional to y. x=12 while y=20. Find y when x is 4.

Solution

x ⍺ k

      y

x = k

      y

12 = k

        20

k = 20 x 12

k = 240

,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

k = 240, y= ?, x = 4.

x = k

      y

4 = 240

        y

y x 4 = 240  x  y   (multiply by y on both sides)

              y

4y = 240

4      4

y = 60.

TRY THIS…………….

x is inversely proportional to y. x=200 while y=4. Find y when x is 80.

LOG 1

Evaluate Log60 – Log0.3 + Log5000.

Solution

= Log60 – Log0.3 + Log5000.

= Log(60 x 5000)

               0.3

= Log(300000)

             0.3

= Log(3,000,000)

              3

= Log 1,000,000

             

= Log₁₀1,000,000

= Log₁₀10⁶

            

= 6Log₁₀10

= 6 x 1

= 6

∴ Log60 – Log0.3 + Log5000 = 4

TRY THIS……………………….

Evaluate Log6000 – Log4.8 + Log80,000