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

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

Solve the following:
log 7 + log (3x - 2) =  log (x + 3) + 1

Solve the following:
log ( x + 1) + log ( x - 1) = log 11 + 2 log 3

Solve the following:
log ₄ x + log ₄ (x-6) = 2

Solve the following:
log ₈ (x² - 1) - log ₈ (3x + 9) = 0

Solve the following:
log (x + 1) + log (x - 1) = log 48

Solve the following:
`log_2x + log_4x + log_16x = (21)/(4)`

Solve for x: log (x + 5) = 1

Solve for x: `("log"27)/("log"243)` = x

Solve for x: `("log"81)/("log"9)` = x

Solve for x: `("log"121)/("log"11)` = logx

Solve for x: `("log"125)/("log"5)` = logx

Solve for x: `("log"128)/("log"32)` = x

Solve for x: `("log"1331)/("log"11)` = logx