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

If log ₃ m = x and log ₃ n = y, write down
`3^(1-2y+3x)` in terms of m an n

Find x and y, if `("log"x)/("log"5) = ("log"36)/("log"6) = ("log"64)/("log"y)`

If `"log" x^2 - "log"sqrt(y)` = 1, express y in terms of x. Hence find y when x = 2.

If 2 log x + 1 = log 360, find: x

If 2 log x + 1 = log 360, find: log(2 x -2)

If 2 log x + 1 = log 360, find: log (3 x² - 8)

If x + log 4 + 2 log 5 + 3 log 3 + 2 log 2 = log 108, find the value of x.

If a = `"log" 3/5, "b" = "log" 5/4 and "c" = 2 "log" sqrt(3/4`, prove that 5^a+b-c = 1

Express the following in a form free from logarithm:
3 log x - 2 log y = 2

Express the following in a form free from logarithm:
2 log x + 3 log y = log a

Express the following in a form free from logarithm:
m log x - n log y = 2 log 5

Express the following in a form free from logarithm:
`2"log" x + 1/2"log" y` = 1

Express the following in a form free from logarithm:
5 log m - 1 = 3 log n

Prove that log (1 + 2 + 3) = log 1 + log 2 + log 3. Is it true for any three numbers x, y, z?

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

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

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

Prove that log ₁₀ 125 = 3 (1 - log ₁₀ 2)

Prove that `("log"_"p" x)/("log"_"pq" x)` = 1 + log_p q

Prove that: `(1)/("log"_2 30) + (1)/("log"_3 30) + (1)/("log"_5 30)` = 1