Question

What is the true solution to the equation below? 2 in e in2×-in e in 10×= in 30 A x=30 B x=75 C x=150 D x=300

Answer 1

b x=75

Explanation:

Answer 2

Option B.

Explanation:

Let as consider the given equation:

`2\ln e^(\ln 2x)-\ln e^(\ln 10x)=\ln 30`

It can be written as

`2(\ln 2x)-(\ln 10x)=\ln 30`
`[\because \ln e^a=a]`

`\ln (2x)^2-(\ln 10x)=\ln 30`
`[\because \ln a^b=b\ln a]`

`\ln (4x^2)/(10x)=\ln 30`
`[\because \ln (a)/(b)=\ln a-\ln b]`

`\ln (2x)/(5)=\ln 30`

On comparing both sides, we get

`(2x)/(5)=30`

Multiply both sides by 5.

`2x=150`

Divide both sides by 2.

`x=75`

Therefore, the correct option is B.