Solve the equation. round to the nearest hundredth. show work.

x = 0.92

Step-by-step explanation:

To solve this, we need first use the exponent rule of    on .  We can break it down to  . We can now re-write as:

This looks like a trinomial that we can middle term factorize by letting . Thus we can write and factorize and solve as shown below:

Thus, 2y-5 = 0 OR 3y+1 = 0

Solving we have  y = 5/2 and y = -1/3

Now bringing back the original variable of letting y = e^x, we have:

1. 5/2 = e^x, and

2. -1/3 = e^x

Solving 1:

Solving 2:

We will have x = ln (-1/3) WHICH IS NOT POSSIBLE because ln is never negative.

So our answer is x = ln (5/2)

Rounding to nearest hundredth: x = 0.92

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