Exponential and logarithmic properties

[fisico]

Hi. I'm having trouble solving for t:

1180 = 98t + 1080e^(-t/10)

I know basic properties but I think I am not remembering some idea or specific property to be able to solve this. Thank you for any help.

 

[HallsofIvy]

Since the variable, t, appears both "inside" an exponential and "outside" there is no elementary function that will reduce that equation. You might look at "Lambert's W function" (check
http://en.wikipedia.org/wiki/Lambert's_W_function) which is defined[\b] as the inverse of the function f(x)= xe^x.
A variation of that will "solve" your equation.

 

[Architeuthis Dux]

Hi there,

It looks like you are trying to solve for t in an exponential and logarithmic equation. In order to solve this, you will need to use both exponential and logarithmic properties.

First, let's rearrange the equation to get all the terms with t on one side:

98t = 1180 - 1080e^(-t/10)

Now, we can use the logarithmic property that states log(a^b) = b*log(a). In this case, a is the base of the exponential function, which is e. So we can rewrite the equation as:

98t = 1180 - 1080*10^(log(e)*(-t/10))

Next, we can simplify the logarithm term using the property log(e) = 1:

98t = 1180 - 1080*10^(-t)

Now, we can use the property that states a^(-b) = 1/a^b to rewrite the equation as:

98t = 1180 - 1080*(1/10^t)

Finally, we can solve for t by dividing both sides by 98 and then using a calculator to find the value of t:

t = (1180 - 1080*(1/10^t))/98

I hope this helps you solve the equation. Remember to always use the properties of exponential and logarithmic functions to help you solve these types of equations. Good luck!