I'm working on some data which use length and height and return one value.
Something like :
And I would like an equation that use the width and the height as parameters to have an approximate number of the value in the table.
For example Width: $50$ and Height: $60$ would return something close to $4,2$.
I tried to make some tendency curves in excel for each line which would give me something like :
For width: $20$ my result is $-2,745 \ln(x) + 16,159$
For width: $120$ my result is $-0,715 \ln(x) + 6,075$
Would it be possible to turn those into one equation using $x$ (width) and $y$ (height) or something similar ?
There are many ways of finding a function which fits the data well enough. Some of them provide perfect fit but at the cost of the function being very complicated and jumping up and down quite wildly between the given data points, others sacrifice exact matches but provide much simpler functions.
Depending on the actual problem you are trying to solve, you might already have some pre-existing assumption about the suitable building blocks of the function and only need to fine-tune their combination. This is exactly what Excel did when you asked it about the trend line: It applied an approach named Linear regression and since you chose the logarithmic variant of the trend line, it looked for an expression of the form $$A+B\ln(x)$$ and sought the optimal values of $A$ and $B$ to minimize the difference between the given values and the ones provided by the formula. Internally, it was minimizing sum of squares of the differences and, unsurprisingly, the method is actually named Method of Least Squares. The same approach can be used for optimizing expressions based on multiple variables and it is usually called multiple linear regression. From mathematical point of view, it is not really that much different.
However, I am not an Excel expert and I don't know if it can be performed easily within it; unlike the simple "linear", "logarithmic" or "exponential" trend-lines which are clear enough as expressions, with more than one variable, you would end up with too many different variants to describe them easily. Having said that, there are some simplistic approaches that one can do directly in Excel (even though they might far from optimal); one example of such looks as follows.
Just as you used Excel to get the trend-lines of your chosen form for two of the fixed values of one parameter, you can do the same for the others too. This will give you six (if you vary height) or eight (for each value of width) trend-lines; each of them described by two values (if you keep using the logarithmic ones). Now you can gather the first coefficient from each trend-line and try to see what trend-line approximates these coefficients well enough and repeat the same for the second set of coefficients, getting another trend-line. Note that these coefficients-related trend-lines do not need to be of the same type as the initial ones; they can even be each its own separate type.
Interestingly, when I used my Excel with your data, it provided me trend-lines different from those you listed (of course, I might have made a typo here and there while retyping the values from your table). In the following example, I varied the height and got the following six lines: $$\begin{eqnarray} 20 & : & -2.92\ln({\rm width}) + 16.71\\ 40 & : & -1.61\ln({\rm width}) + 10.88\\ 60 & : & -1.05\ln({\rm width}) + 8.44\\ 80 & : & -0.85\ln({\rm width}) + 7.53\\ 100 & : & -0.75\ln({\rm width}) + 6.73\\ 120 & : & -0.68\ln({\rm width}) + 5.95 \end{eqnarray}$$
Now, the best-looking trend-line for values $-2.92, -1.61, \ldots, -0.68$ (as corresponding to heights $20$, $40, \ldots, 120$) seems to be of the form $$-34.8\times {\rm height}^{-0.84}$$ and the one for the second coefficients ($16.71, 10.88, \ldots, 5.95$) comes out as $$89.23\times {\rm height}^{-0.57}$$
Putting it all together, one possible approximation of all the data in the table would be $$-34.8\times {\rm height}^{-0.84}\times \ln({\rm width})+89.23\times {\rm height}^{-0.57}$$
Of course, this approach approximates the approximate values, so it accumulates the errors coming from each individual trend-line and adds further error terms due to matching their coefficients only approximately. Moreover, depending on the type of problem you are looking into, this particular expression might be completely useless for practical use. However, in order to be able to provide a more relevant expression, it would be necessary to get better understanding of the meaning of the data.