Answer:
Option B. x = 75
Step-by-step explanation:
The given equation is
[tex]2 ln e^{ln2x}-ln e^{ln 10x}=ln 30[/tex]
[ since [tex]ln e^{x}= x lne[/tex] ]
[tex]2(ln2x)ln e-(ln10x)ln e=ln 30[/tex]
[ since ln e = 1 ]
2ln (2x) - ln (10x) = ln 30
ln (2x)² - ln (10x) = ln 30
ln 4x² - ln 10x = ln 30
[ since [tex]lna-lnb=ln\frac{a}{b}[/tex] ]
[tex]ln\frac{4x^{2}}{10x}=ln 30[/tex]
[tex]\frac{4x^{2} }{10x}=30[/tex]
[tex]4x^{2}=300x[/tex]
4x = 300
[tex]x=\frac{300}{4}=75[/tex]
Option B. x = 75 is the answer.
