Question

In Exercises 43-46, solve the equ
43. 33x+6=27* +2

Answer 1

2x+6=2x+2
4x=+2-6
4x=-4
X=-1

Answer 2

43. All real numbers

44. x = 1/4

45. No solution

Explanation:

The technique here is two write two expressions with the same base that are equal. Then set the exponents equal and solve for the variable.

43.

`3^(3x + 6) = 27^(x + 2)`

`3^(3x + 6) = (3^3)^(x + 2)`

`3^(3x + 6) = 3^(3(x + 2))`

`3^(3x + 6) = 3^(3x + 6)`

`3x + 6 = 3x + 6`

Answer: all real numbers

44.

`3^(4x + 3) = 81`

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

`4x + 3 = 4`

`4x = 1`

`x = (1)/(4)`

45.

`4^(x + 3) = 2^(2(x + 1))`

`(2^2)^(x + 3) = 2^(2(x + 1))`

`2^(2(x + 3)) = 2^(2(x + 1))`

`2(x + 3) = 2(x + 1)`

`x + 3 = x + 1`

`3 = 1`

No solution.