# Thread: need help

1. ## need help

i have 31.6 = 12.74(Z - 18.63)^1.15

and i need to find Z

i get 20.01

can any1 confirm this?

2. Originally Posted by question
i have 31.6 = 12.74(Z - 18.63)^1.15

and i need to find Z

i get 20.01

can any1 confirm this?
Let us see.

31.6 = (12.74)(z -18.63)^(1.15)
31.6 / 12.74 = (z -18.63)^(1.15)
2.480377 = (z -18.63)^(1.15)
Raise both sides to their 1/(1.15) power,
2.203225 = z -18.63
2.20 +18.63 = z
z = 20.83 ---------------answer.

Uh-oh, that's not 20.01. It is close, though.

3. Originally Posted by question
i have 31.6 = 12.74(Z - 18.63)^1.15

and i need to find Z

i get 20.01

can any1 confirm this?
$\displaystyle 31.6=12.74(z-18.63)^{1.15}$

divide through by $\displaystyle 12.74$:

$\displaystyle 31.6/12.74\approx 2.4804 \approx (z-18.63)^{1.15}$

Now take logs:

$\displaystyle \ln(2.4804) \approx 1.15 \ln(z-18.63)$

rearrange and simplify:

$\displaystyle \ln(z-18.63) \approx \ln(2.4804)/1.15 \approx 0.78993$

so:

$\displaystyle z-18.63 \approx e^{ 0.78993}$

so:

$\displaystyle z \approx 18.63+e^{ 0.78993}\approx 20.833$

RonL