Question

solve for x if 3 ^x-1 =1/27

Answer 1

${3}^{(x - 1)} = \frac{1}{27} \\ \\ {3}^{(x - 1)} = \frac{1}{ {3}^{3} } \\ \\ {3}^{(x - 1)} = {3}^{ - 3} \\ \\ \text{comparing powers of 3 on both sides} \\ \\ x - 1 = - 3 \\ \\ x = - 3 + 1 \\ \\ \boxed{ \large{x = - 2}}$

Answer 2

Answer:

The value of x = -2.

Step-by-step explanation:

Bases and Exponents:

• Base number is defined as a number which is multiplied by itself, whereas the exponent represents the number of times the base number is multiplied.
• In short, Power is a number expressed using the exponents. It implies the repeated multiplication of the same factor.

       Given equation is

                   (3)^x-1 = 1/27

      we will convert the above equation in R.H.S in terms of power of 3.

                   (3)^x-1 = 1/((3)^3)

                   (3)^x-1 = (3)^-3

      By powers and exponents rule,

      If bases are equal then exponents are equal.

                        x-1 = -3

                          x = -3+1

                          x = -2

          Hence the value of x = -2.

Know more about Solving Algebraic equations:

https://brainly.in/question/21098904?referrer=searchResults