Question

See the attachment below for the question.

Answer 1

Answer: Third option.

Step-by-step explanation:

We need to remember that:

$a^m=a^n\\\\m=n$

In this case, given this expression:

$4^x$$=8^{( x- 1)}$

We need to descompose 4 and 8 into their prime factors:

$4=2*2=2^2$

$8=2*2*2=2^3$

Rewriting the expression:

$2^{2x}$$=2^{3(x - 1) }$

Then:

$2x = 3(x - 1)$

Finally, applying Distributive property on the right side and solving for "x", we get:

$2x=3x-3\\\\3=3x-2x\\\\x=3$

Answer 2

Answer:

The correct answer is third option

x = 3

Step-by-step explanation:

It is given that,

4ˣ = 8⁽ˣ ⁻ ¹⁾

To find the value of x

4ˣ  = (2²)ˣ

8⁽ˣ ⁻ ¹⁾ = (2³)⁽ˣ ⁻ ¹⁾

4ˣ = 8⁽ˣ ⁻ ¹⁾

(2²)ˣ =  (2³)⁽ˣ ⁻ ¹⁾

2²ˣ = 2⁽³ˣ ⁻ ³⁾

2x = 3x - 3

3x - 2x = 3

x = 3

The correct answer is third option

x = 3