Evaluate the Following: ( 1 − 15 64 ) − 1 2 - Mathematics

Evaluate the following:

`(1 - 15/64)^(-1/2)`

योग

`(1 - 15/64)^(-1/2)`

= `((64 - 15)/64)^(-1/2)`

= `(49/64)^(-1/2)`

= `(64/49)^(1/2)`

= `(8)/(7)`.

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Solving Exponential Equations

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अध्याय 9: Indices - Exercise 9.1

अध्याय 9 Indices
Exercise 9.1 | Q 6.1

Solve : `[3^x]^2` : 3x = 9 : 1

Solve for x : `(81)^(3/4) - (1/32)^(-2/5) + x(1/2)^(-1).2^0 = 27`

Solve for x : 3(2^x + 1) - 2^{x + 2} + 5 = 0

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

Evaluate the following:

`(4^3 xx 3^7 xx 5^6)/(5^8 xx 2^7 xx 3^3)`

Evaluate the following:

`sqrt(1/4) + (0.01)^(-1/2) - (27)^(2/3)`

Solve for x:
`9 xx 3^x = (27)^(2x - 5)`

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

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

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