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

If a² + b² = 23ab, show that:

log `(a + b)/5 = 1/2`(log a + log b).

If log_√27x = 2 `(2)/(3)` , find x.

If m = log 20 and n = log 25, find the value of x, so that :
2 log (x - 4) = 2 m - n.

Solve for x and y ; if x > 0 and y > 0 ; log xy = log `x/y` + 2 log 2 = 2.

Find x, if :  log_x 625 = - 4

Find x, if : log_x (5x - 6) = 2

Show that : log_a m ÷ log_ab m + 1 + log _ab 

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)`.