-8.2.59 Find eq for level surface

[karush]

$\tiny{x4.01}$
$\textsf{Find an equation for the level surface of the function}$
$$f(x,y,z)=x+e^{y+z}$$
$\textsf{ that passes through the point}$
$$(1, \ln(4), \ln(9))$$

 

[MarkFL]

Basically, you want:

\(\displaystyle f(x,y,z)=f\left(1,\ln(4),\ln(9)\right)\)

So, what do you get?

 

[karush]

Basically, you want:

\(\displaystyle f(x,y,z)=f\left(1,\ln(4),\ln(9)\right)\)

So, what do you get?

plug in would be

$f(1,\ln(4),\ln(9))=1+e^{\ln(4)+\ln(9)}=1+4 \cdot 9 =37$

 

[MarkFL]

plug in would be

$f(1,\ln(4),\ln(9))=1+e^{\ln(4)+\ln(9)}=1+4 \cdot 9 =37$

Yes, so the equation of the level surface would be:

\(\displaystyle x+e^{y+z}=37\)