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Exercise

$e^x+e^y+e^z=25$

Step-by-step Solution

1

We need to isolate the dependent variable $y$, we can do that by simultaneously subtracting $e^x+e^z$ from both sides of the equation

$e^y=25-\left(e^x+e^z\right)$
2

Simplify the product $-(e^x+e^z)$

$e^y=25-e^x-e^z$
3

We can take out the unknown from the exponent by applying natural logarithm to both sides of the equation

$\ln\left(e^y\right)=\ln\left(25-e^x-e^z\right)$
4

Apply the formula: $\ln\left(e^x\right)$$=x$, where $x=y$

$y=\ln\left(25-e^x-e^z\right)$

Final answer to the exercise

$y=\ln\left(25-e^x-e^z\right)$

Try other ways to solve this exercise

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  • Derivative
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