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

If 2400 = 2^x x 3^y x 5^z, find the numerical value of x, y, z. Find the value of 2^-x x 3^y x 5^z as fraction.

If 2^x = 3^y = 12^z ; show that `(1)/z = (1)/y + (2)/x`.

Find the value of 'a' and 'b' if:

9^2a = `(root(3)(81))^(-6/"b") = (sqrt(27))^2`

Find the value of 'a' and 'b' if:

`(sqrt243)^"a" ÷ 3^("b" + 1)` = 1 and `27^"b" - 81^(4 -"a"/2)` = 0

Prove the following:

`sqrt(x^-1 y) · sqrt(y^-1 z) · sqrt(z^-1 x)` = 1

Prove the following:

`(x^("a"+"b")/x^"c")^("a"-"b") · (x^("c"+"a")/(x^"b"))^("c"-"a") · ((x^("b"+"c"))/(x"a"))^("b"-"c")` = 1

Prove the following:

`("a"^"m"/"a"^"n")^("m"+"n"+1) ·("a"^"n"/"a"^1)^("n" + 1-"m").("a"^1/"a"^"m")^(1+"m"-"n")`

Prove the following:

`root("ab")(x^"a"/x^"b")·root("bc")(x^"b"/x^"c")·root("ca")(x^"c"/x^"a")` = 1

Prove the following:
(x^a)^b-c x (x^b)^c-a x (x^c)^a-b = 1

Prove the following:

`(x^("p"("q"-"r")))/(x^("q"("p"-"r"))) ÷ (x^"q"/x^"p")^"r"` = 1

Express the following in the logarithmic form:
3³ = 27

Express the following in the logarithmic form:
5⁴ = 625

Express the following in the logarithmic form:
9⁰ = 1

Express the following in the logarithmic form:

`(1)/(8)` = 2^-3 

Express the following in the logarithmic form:
11² = 121

Express the following in the logarithmic form:

3^-2 = `(1)/(9)`

Express the following in the logarithmic form:
10^-4 = 0.0001

Express the following in the logarithmic form:
7⁰ = 1

Express the following in the logarithmic form:

`(1/3)^4 = (1)/(81)`

Express the following in the logarithmic form:

9^-4 = `(1)/(6561)`