Solve-for-x-x-log-3-2-x-1-

Question Number 55806 by Tawa1 last updated on 04/Mar/19

Solve for x : x^{\log_{3} 2} = \sqrt{x} + 1

Answered by MJS last updated on 04/Mar/19

\ln x^{\log_{3} 2} = \ln x^{\frac{\ln 2}{\ln 3}} = \frac{\ln 2}{\ln 3} \ln x =

[let x = 3^{t}]

= t \ln 2

e^{t \ln 2} = 2^{t}

2^{t} = 3^{\frac{t}{2}} + 1

\Rightarrow for t = 2 n both sides are real

4^{n} = 3^{n} + 1 \Rightarrow n = 1 \Rightarrow t = 2 \Rightarrow x = 9

Commented by Tawa1 last updated on 04/Mar/19

God bless you sir

Facebook Tweet Pin