LOGARITHMS B15

If Log_ax = 13, find Log_a(¹/x)

Solution

= Log_a(¹/x)

= Log_ax^-1

= -1 x Log_ax

= -1 x 13

= -13

TRY THIS………..

If Log_aW= 26, find Log_a(¹/W)

ARITHMETIC PROGRESSION C3

The 1st term of an A.P. is 80 and the common difference is 24. Find the 10th term.

Solution

A₁= 80, d = 24

A_n = A₁ + (n-1)d

A₁₀ = A₁ + (10-1)d

A₁₀ = A₁ + 9d

A₁₀ = 80 + (9x24) [ after substituting A₁= 80, d = 24 as given above]

∴ A₁₀ = 80 + 216

A₁₀ = 296

Hence the 10th term is 296.

TRY THIS……………

The 1st term of an A.P. is 17 and the common difference is 33. Find the 8th term.

FUNCTIONS B13

If F(x) = 8x + 10; Find F^-1(x).

Solution

HINT: F^-1(x) means inverse.

PROCEDURE:

Make x the subject and then interchange x and y variables.

Let y=F(x)

So,  y= 8x + 10

y – 10 = 8x

y – 10  = 8x

   8          8

y – 10   = x

   8

x  =   y – 10     after rearranging

           8

 y^-1 = x – 10     after interchanging x and y variables.

             8

F^-1(x) = x – 10     after interchanging x and y variables.

                8

Hence, F^-1(x) = x – 10     

                              8

TRY THIS……………………………

If F(x) = 7x + 20; Find F^-1(x).

LOGARITHMS B14

If log 2= 0.3010; find the value of log 25 without using tables.

solution

log25=log(100÷ 4)

=log100 - log4

=log10² – log2²

=2log10 – 2log2

=(2x1) – 2(0.3010)

=2– 2(0.3010)

=2 – 0.6020

=1.398

Hence log25=1.398

TRY THIS……………

If log 2= 0.3010; find the value of log 25 without using tables.

CIRCLES C11

Find the value of <PRN in the figure below.

Solution

<PMR = <PNR ( angles subtended by the same arc are equal)

<PMR = 68⁰

so, <PMN = 68⁰ + 36⁰

                = 104⁰

<PMN + <PRN = 180⁰ (opposite angles in a cyclic quadrilateral add up to 180)

∴ 104⁰ + <PRN = 180⁰

∴  <PRN = 180⁰ - 104⁰

∴  <PRN = 76⁰