Question

What is the true solution to the equation below?

Answer 1

2 ln e^ln2x = 2 ln 2x
ln e^ln10x = ln 10x
so
2 ln 2x - ln 10x = ln 30
ln (2x)^2 - ln 10x = ln 30
ln ( 4x^2 / 10x) = ln 30
4x^2 / 10x) = 30
0.4x = 30
x = 30 / 0.4 = 75 answer

Answer 2

Option B. x = 75

Explanation:

The given equation is

`2 ln e^(ln2x)-ln e^(ln 10x)=ln 30`

[ since
`ln e^(x)= x lne` ]

`2(ln2x)ln e-(ln10x)ln e=ln 30`

[ since ln e = 1 ]

2ln (2x) - ln (10x) = ln 30

ln (2x)² - ln (10x) = ln 30

ln 4x² - ln 10x = ln 30

[ since
`lna-lnb=ln(a)/(b)` ]

`ln(4x^(2))/(10x)=ln 30`

`(4x^(2) )/(10x)=30`

`4x^(2)=300x`

4x = 300

`x=(300)/(4)=75`

Option B. x = 75 is the answer.