Question

Solve for x.

4 In (5x)= 20

Do not round any intermediate computations, and round your answer to the nearest hundredth.

x

5

?

Answer 1

x ≈ 29.68 to the nearest hundredth

Explanation:

To solve for x in the equation; 4 In (5x) = 20, we need to follow the steps below:

4 In (5x) = 20

First divide both-side of the equation by 4

4 In(5x) /4 = 20/4

(On the left-hand side of the equation, 4 at the numerator will cancel out 4 at the denominator leaving us with just In (5x) while at the right-hand side of the equation 20 will be divided by 5 to give us 5). Thus our equation becomes;

In (5x) = 5

Take the exponential of both-side

`e^(In (5x))` =
`e^(5)`

At the left-hand side of the equation e will cancel-out In, hence;

5x =
`e^(5)`

5x = 148.4131591025766

Divide both-side of the equation by 5

`(5X)/(5)` =
`(148.4131591025766)/(5)`

x =29.682631820515322

x ≈ 29.68 to the nearest hundredth