How do you solve 8^(x-1)=root3(16)8x1=316?

1 Answer
May 24, 2016

x=13/9x=139 or x=1 4/9x=149

Explanation:

To solve 8^(x-1)=root(3)168x1=316

We begin by taking the 1616 out of the root

8^(x-1)=16^(1/3)8x1=1613

Next convert the 88 and 1616 to the same base.

(2^3)^(x-1)=(2^4)^(1/3)(23)x1=(24)13

Now simplify the exponents

2^(3x-3) = 2^(4/3)23x3=243

Since the base values are the same we can simply simplify the exponents algebraically.

3x-3 =4/33x3=43

3xcancel(-3) cancel(+3) =4/3 + 3

3x = 13/3

cancel3x (1/cancel3)= 13/3(1/3)

x=13/9 or x=1 4/9