# 4^(x-1) =8*2^3x    find x.

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

Since 8 is a power of 2, we'll write it as:

8  =2^3

Now, we'll apply the multiplication rule of 2 exponentials that have matching bases:

2^3*2^3x = 2^(3 + 3x)

We'll re-write the equation, putting 4 = 2^2

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

Since the bases are matching, we'll apply one to one rule:

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

We'll open the brackets:

2x - 2 = 3x + 3

We'll subtract 2x - 2 and we'll apply symmetrical property:

3x + 3 - 2x + 2 = 0

x + 5 = 0

We'll subtract 5:

x = -5

The solution of the equation is x = -5.

neela | High School Teacher | (Level 3) Valedictorian

Posted on

4^(x-1) =8*2^3x.  Find x.

We replace 4 = 2^2 and 8 = 2^3 in the given equation.

(2^2)^(x-1) = (2^3)*2^3x.

2^2(x-1) = 2^(3 +3x), as (a^m)^n = a^(mn). And a^m*a^n  a^(m+n) by index law.

Now both sides of the equation have the same base 2. So we equate the exponents:

2(x-1) = 3+3x.

2x-2 = 3+3x.

-2-3 = 3x-2x = x.

Threfore x = -5.