(English Medium) ICSE Class 9 - CISCE Question Bank Solutions for Mathematics

If p = log 20 and q = log 25 , find the value of x , if 2log( x + 1 ) = 2p - q. 

If log₂(x + y) = log₃(x - y) = `log 25/log 0.2`, find the values of x and y.

Given : `log x/ log y = 3/2` and log (xy) = 5; find the value of x and y.

Given log₁₀x = 2a and log₁₀y = `b/2`. Write 10^a in terms of x.

Given log₁₀x = 2a and log₁₀y = `b/2`. Write 10^{2b + 1} in terms of y.

Evaluate: log_b a × log_c b × log_a c.

Given log₁₀x = 2a and log₁₀y = `b/2. "If"  log_10^p = 3a - 2b`, express P in terms of x and y.

Solve : log₅( x + 1 ) - 1 = 1 + log₅( x - 1 ).

Solve for x, if : log_x49 - log_x7 + log_x `1/343` + 2 = 0

Evaluate :  log₃8 ÷ log₉16 

If a² = log x , b³ = log y and `a^2/2 - b^3/3` = log c , find c in terms of x and y.

Given x = log₁₀12 , y = log₄ 2 x log₁₀9 and z = log₁₀0.4 , find :
(i) x - y - z
(ii) 13^{x - y - z}

Solve for x, `log_x^(15√5) = 2 - log_x^(3√5)`.

Evaluate :  `( log _5^8 )/(( log_25 16 ) xx  ( log_100  10))`

In a quadrilateral ABCD, AB = AD and CB = CD.

Prove that:

1. AC bisects angle BAD.
2. AC is the perpendicular bisector of BD.

Prove that the bisectors of the interior angles of a rectangle form a square.

ABCD is a square. A is joined to a point P on BC and D is joined to a point Q on AB. If AP = DQ;

prove that AP and DQ are perpendicular to each other.

Evaluate: `(log_5 8)/(log_25 16 xx Log_100 10)` 

Solve the following:
log (3 - x) - log (x - 3) = 1

Solve the following:
log(x² + 36) - 2log x = 1