Question

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

Answer 1

Answer:

x = 49.84

Step-by-step 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}

⇒ $\ln \ln 5x = \ln 15 -\ln e$

⇒ $\ln \ln 5x=\ln \frac{15}{e}$ {Since we know that ln A/B = ln A - ln B}

⇒ $\ln 5x = \frac{15}{e}$

⇒ $5x = e^{\frac{15}{e} }$

⇒ $x = \frac{1}{5} e^{\frac{15}{e} }${Converting logarithm to exponent form}

⇒ x = 49.84 (Approximate) (Answer)