Question

Question #6daa9

Answer 1

`x = frac{ln(2) + 2}{5}`

Explanation:

Take the natural logarithm on both sides

`ln(e^{3x} * e^{2x-1}) = ln(2e)`

From the identity

`ln(ab) = ln(a) + ln(b)`

We can simplify the above equation as

`ln(e^{3x}) + ln(e^{2x-1}) = ln(2) + ln(e)`

`3x + (2x-1) = ln(2) + 1`

`5x = ln(2) + 2`

`x = frac{ln(2) + 2}{5}`

Answer 2

A slightly different approach

`=>x = (ln(2)+2)/5`

Explanation:

Given:`" "e^(3x) xx e^(2x-1)=2e`

Compare to `10^2xx10^1 = 10^3 =10^(2+1)`

Using the above method we have;

`" "e^(3x) xx e^(2x-1)=2e" "->" "e^(3x+2x-1)=2e`

Divide both sides by `e`

`e^(3x+2x-2)=2`

`=>e^(5x-2)=2`

Take logs of both sides

`(5x-2)ln(e)=ln(2)`

But `ln(e)=1`

`5x-2=ln(2)`

`=>x=(ln(2)+2)/5`