Question

2 In eIn2x - In eIn 10x = In 30
x=30
x=75
x= 150
x=300​

Answer 1

The value of x = 75 ⇒ 2nd answer

Step-by-step explanation:

Let us revise some rules of logarithmic function

• $ln(a) - ln(b)=ln(\frac{a}{b})$
• $e^{ln(a)}=a$
• $ln(a)^{n}=nln(a)$ vice-versa $nln(a)=ln(a)^{n}$
• If ㏑(a) = ㏑(b), then a = b

∵ $2ln(e^{ln(2x)})-ln(e^{ln(10x)})=ln(30)$

- Use the 2nd rule to simplify it

∵ $e^{ln(2x)}=2x$

∵ $e^{ln(10x)}=10x$

∴ 2㏑(2x) - ㏑(10x) = ㏑(30)

- Use the 3rd rule in the 1st term

∵ 2㏑(2x) = ㏑(2x)² = ㏑(4x²)

∴ ㏑(4x²) - ㏑(10x) = ㏑(30)

- Use the 1st rule with the left hand side

∵ $ln(4x^{2})-ln(10x)=ln(\frac{4x^{2}}{10x})$

∴ $ln(\frac{4x^{2}}{10x})=ln(30)$

∵ $\frac{4x^{2}}{10x}=\frac{2x}{5}=\frac{2}{5}x$

∴ $ln(\frac{2}{5}x)=ln(30)$

- Use the 4th rule

∴ $\frac{2}{5}$ x = 30

- Multiply both sides by 5

∴ 2 x = 150

- Divide both sides by 2

∴ x = 75

The value of x = 75

Learn more:

You can learn more about logarithmic functions in brainly.com/question/11921476

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