Question

answer the very easy question and get 49+25 points.

Answer 1

Hey

Here is your answer

(i) Here we use laws of exponents :

Given ( 27 ) ^ x = 9 / 3 ^x

( 3 × 3 × 3 )^x = ( 3 × 3 ) / 3^x
( 3 ³ )^x = 3² / 3^x
3 ^ 3x × 3^x = 3²            [ since  ( a ^m)^n = a ^mn ]
3^ (3x +x) = 3²                [ since a^m × a^n = a ^m+n ]
3^4x = 3²
4x = 2                      [ since  If a ^m = a ^n then m = n ]
x = 2 / 4
  ∴ x = 1 /2

(ii) 2^5x ÷ 2^x = 5√2^2. [ since a^m ÷ a^n = a ^m-n ]
2^5x-x = 5√2^2
2^4x = 5√2^2

Answer 2

Answer:

Step-by-step explanation:

(i) Here we use laws of exponents :

Given ( 27 ) ^ x = 9 / 3 ^x

( 3 × 3 × 3 )^x = ( 3 × 3 ) / 3^x

( 3 ³ )^x = 3² / 3^x

3 ^ 3x × 3^x = 3²            [ since  ( a ^m)^n = a ^mn ]

3^ (3x +x) = 3²                [ since a^m × a^n = a ^m+n ]

3^4x = 3²

4x = 2                      [ since  If a ^m = a ^n then m = n ]

x = 2 / 4

  ∴ x = 1 /2

(ii) 2^5x ÷ 2^x = 5√2^2. [ since a^m ÷ a^n = a ^m-n ]

2^5x-x = 5√2^2

2^4x = 5√2^2