Solve the equation: 27^(1−x)= 81 without using logarithms.

Question

Don't use log

Answer 1

Hi Rosa;

 

First, note that 27 = 3³ and 81 = 3⁴

 

27^(1-x) = 81

(3³)^(1-x) = 3⁴

3^3-3x = 3⁴

3 - 3x = 4

-3x = 1

x = -1/3

 

check:  27^(1-(-1/3)) = 81

            27^4/3 = 81

            (³√27)⁴ = 81

            3⁴ = 81

            81 = 81

 

Answer 2

Now this question is correct.  Rewrite the equation using a common base.

 

(3³)^{(1 - x)} = 3⁴

 

 

Equate exponents.

 

3(1 - x) = 4

 

 

Solve for x.