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)`

योग

`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.

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Solving Exponential Equations

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अध्याय 9: Indices - Exercise 9.1

अध्याय 9 Indices
Exercise 9.1 | Q 6.3

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

If 5^{x + 1} = 25^{x - 2}, find the value of 3^{x - 3} × 2^{3 - x}.

Prove that : `((x^a)/(x^b))^( a + b - c ) (( x^b)/(x^c))^( b + c - a )((x^c)/(x^a))^( c + a - b)`

Evaluate the following:

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

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

Solve for x:

9 x 81^x = `(1)/(27^(x - 3)`

Solve for x:
9^x+4= 3² x (27)^x+1

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

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.

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

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