Question

What is the true solution to 2 In eln 5x – 2 In 15?

Answer 1

x = 49.84

Explanation:

We are given an equation of unknown x and we have to solve the equation for x.

`2\ln(e\ln5x)-2\ln15 =0`

⇒
`ln(e\ln5x) = \ln15`

⇒
`\ln e + \ln \ln 5x = \ln 15` {Since we know that ln AB =ln A + ln B}

⇒
`\ln \ln 5x = \ln 15 -\ln e`

⇒
`\ln \ln 5x=\ln (15)/(e)` {Since we know that ln A/B = ln A - ln B}

⇒
`\ln 5x = (15)/(e)`

⇒
`5x = e^{(15)/(e) }`

⇒
`x = (1)/(5) e^{(15)/(e) }`{Converting logarithm to exponent form}

⇒ x = 49.84 (Approximate) (Answer)