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

Given 2 log₁₀ x + 1 = log₁₀ 250, find :
(i) x
(ii) log₁₀ 2x

If log 2 = 0.3010 and log 3 = 0.4771 ;  find the value of : log 12

If log₁₀2 = a and log₁₀3 = b ; express each of the following in terms of 'a' and 'b': log 2.25

If log 2 = 0.3010 and log 3 = 0.4771 ; find the value of : log 1.2

If log 2 = 0.3010 and log 3 = 0.4771; find the value of : log 15

If log (a + b) = log a + log b, find a in terms of b.

If log₁₀ 8 = 0.90; find the value of : log 0.125

If log₁₀ 8 = 0.90; find the value of : log√32

Prove that :  (log a)² - (log b)² = log `(( a )/( b ))` . Log (ab)

If log 27 = 1.431, find the value of : log 9

If log 27 = 1.431, find the value of : log 300

Prove that :  If a log b + b log a - 1 = 0, then b^a. a^b = 10

If log₁₀ a = b, find 10^{3b - 2} in terms of a.

 If log (a + 1) = log (4a - 3) - log 3; find a.

If log₅ x = y, find 5^{2y+ 3} in terms of x.

If 2 log y - log x - 3 = 0, express x in terms of y.

Given: log₃ m = x and log₃ n = y.
Express 3^{2x - 3} in terms of m.

Given: log₃ m = x and log₃ n = y.

Write down `3^(1 - 2y + 3x)` in terms of m and n.

Given: log₃ m = x and log₃ n = y.
If 2 log₃ A = 5x - 3y; find A in terms of m and n.

Prove that:

log₁₀ 125 = 3(1 - log₁₀2).