Evaluate the Following: 9 5 2 − 3 × 5 0 − ( 1 81 ) − 1 2 - Mathematics

Evaluate the following:

`9^(5/2) - 3 xx 5^0 - (1/81)^((-1)/2)`

Sum

`9^(5/2) - 3 xx 5^0 - (1/81)^((-1)/2)`

= `3^(2 xx 5/2) - 3 xx 1 - (1/81)^((-1)/2)`

= `3^5 - 3 - 9^(2 xx 1/2)`
= 243 - 3 - 9
= 231.

shaalaa.com

Solving Exponential Equations

Is there an error in this question or solution?

Chapter 9: Indices - Exercise 9.1

Chapter 9 Indices
Exercise 9.1 | Q 6.3

Solve for x:

`3^(4x + 1) = (27)^(x + 1)`

Find x, if : 4^2x = `1/32`

Solve for x : (a^{3x + 5})². (a^x)⁴ = a^{8x + 12}

If a^x = b^y = c^z and b² = ac, prove that: y = `[2xz]/[x + z]`

If a^x = b, b^y = c and c^z = a, prove that : xyz = 1.

Evaluate : `[(-2/3)^-2]^3 xx (1/3)^-4 xx 3^-1 xx 1/6`

If `root(x)("a") = root(y)("b") = root(z)("c")` and abc = 1, prove that x + y + z = 0

If a^x = b^y = c^z and abc = 1, show that

`(1)/x + (1)/y + (1)/z` = 0.

If `x^(1/3) + y^(1/3) + z^(1/3) = 0`, prove that (x + y + z)³ = 27xyz

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