Question

What is the solution to 2 In x = 4 In 2?
x =
DONE

Answer 1

4

Explanation:

Use the property of logarithms
`n\ln x = \ln x^n`. (The number in front of ln becomes an exponent--or vice versa!)

Using that property on both sides, you get

`ln(x^2) = ln(2^4)`

But that means

`x^2=4^2\\x^2=16\\x=4`

Notice that
`x=-4` is not a solution because
`\ln(-4)` is undefined. Negative numbers do not have logarithms. The domain of
`\ln x` is the set of positive numbers.

Answer 2

x =4

Explanation:

2 ln x = 4 ln 2

Divide each side by 2

2/2 In x = 4/2 In 2

ln x = 2 ln 2

Remember that a ln b = ln b^a

ln x = ln 2^2

ln x = ln 4

We are taking the natural log on both sides so , what we are taking the natural log of must be the same

x =4