MATHEMATICS FREE QUESTIONS ON INDICES AND LOGARITHM

By Ibkemmanuel 2021-10-15 EDUCATION 0 Comments

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(a) Find the value of x if: $3x+43- x-32= 3x+13- 2x+54$

(b) solve the following Quadratic Equations using factorization method

$3x2 -5x+2=0$
$2x-3x-2=0$

(a) (i) Simplify: $3x+2×9x-12√27x-1$ (ii) find the value of x if: $2x-3×4x+11442x-1=4x+1$ (b) Find the value(x) of $x$ in the following:

$2x-3×4x+18x-3÷2x-1=4x+1$
$(0.25)x+1×(0.5)x+1(0.125)x+1×2x-1=8x+1$
$4x+2-7.2x-1-2=14$
$2x+2-5.2x+1+3.2x2x+1-3.2x+2-2x=$ $-1117x+2$

Find the value of $x$ in terms of $y and z.$ $2x=3y=6z$

(b) Find $x$ if (i) $2x-1=31-x$ $ii2x+3=6$ given that $log23=1.2$

Simplify:

$log24-log100.1+log279 if log23x$
$4-log42x=log255 find x$
$3log3x-log3x=3$
$2log2x-logx2=1$
$log24x-1-loglog3x-1=2$
$logx2=0.2101 logx3=0.4021 logx5=0.604$ Evaluate: (a) $logx1.5$ (b) $logx2.5$ (c) $log7.5$ (d) $logx72$

Evaluate the following:

i. $27+23-50+147363-243+200+32$ ii. $p=23-32, Evaluate: p2+2p-5$
$If 53-22 43+2=P+Q6$ , Evaluate: $PQ$

Given that f(x) = $3x-42-5x$ and g(x) = $2x2+3x-72x-4$ find: (i)f(2) (ii) f(-3) (iii) f( $-3x-22x+3$ )
(a) A man 1.6m tall is 10m away from a tree 9.0m high. What is the angle of elevation of the top of the tree from the top of his head? (b) Find the equation of the perpendicular bisector of the line joining P(2, -3) to Q(-5, -1) (c) If the bearing of A to B is 060o abd the bearing of A to C is S0oE. if the distance AB and AC are 10km and 12km respectively how far is line BC? (d) A sailor leaves port X to Y on a bearing of 1400 and covers a distance of 7.5km. He then proceeds to Z on a bearing of 2300 and covers a distance of 18km. How far is port Z from X? (e) Five years ago, a father was four times as old as his son. In five years time he will be 10 greater than twice of his son in age. Find the sum of their ages in 3years time

(a) Find the equation of line perpendicular to a line whose gradient is $23$ and passes through the point (-1,2) (b) given the following points A(-2,1), B(2,3) and C(4,5) verify if the points are co-linear otherwise find the area of triangle formed (c) find the equation of locus for the two points A(-3,4) and B(1,-1) (d) find the perpendicular distance of the line 2y + 3x -7=0 from the point P(1.5, 2)

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