# Question #9ce73

##### 2 Answers

This equality cannot be solved for

#### Explanation:

Using log laws we can simplify somewhat and get the

I don't even think this form is simpler than the original, I'm not sure if it's worth doing... But more importantly, how do we know whether we can actually solve for

Let's set:

Setting the two equations equal to each other will allow you to solve for the t values where the two graphs intersect (this is what the original question asked). You should be able to visually find these as the point(s) where the two graphs cross each other.

So let's plot the two together and have a look.

As t goes to negative

So, I can't simplify the original equality any further and solve for

See below.

#### Explanation:

Applying

This equation has the structure

with

Now using the Lambert function

https://en.wikipedia.org/wiki/Lambert_W_function

such that

We will transform

into a suitable form to be handled with the Lambert function so making

then

This gives a complex solution which is