Solve algebraically, showing each step of your working, the equation (8^(x-1) )^2-18(8^(x-1) )+32=0(8x1)218(8x1)+32=0??

1 Answer
Feb 24, 2018

x=4/3x=43 or x=7/3x=73

Explanation:

What we have here is a quadratic equation in terms of 8^(x-1)8x1

Let u=8^(x-1)u=8x1

The equation becomes

u^2-18u+32=0u218u+32=0

(u-16)(u-2)=0(u16)(u2)=0

u=16u=16 or u=2u=2

8^(x-1)=28x1=2 or 8^(x-1)=168x1=16

Considering 8^(x-1)=28x1=2 first;

In log form;

log_8(2)=x-1log8(2)=x1
x-1=1/3x1=13
x=4/3x=43

Consider now 8^(x-1)=168x1=16

In log form;

log_8(16)=x-1log8(16)=x1
x-1=4/3x1=43
x=7/3x=73

So x=4/3x=43 or x=7/3x=73