Thread: Help me with log. tmr exam!

lgx+ln2x=3
solve the eqn
thanks

Hello helloying

Originally Posted by helloying

lgx+ln2x=3
solve the eqn
thanks

I assume that lgx means $\displaystyle \log_{10}x$ and ln2x means $\displaystyle \log_e2x (= \log_e2 + \log_ex)$.

In which case, you need to know that $\displaystyle \log_{10}x = \frac{\log_ex}{\log_e10}$. So the equation becomes:

$\displaystyle \frac{\log_ex}{\log_e10} + \log_e2 + \log_ex = 3$

$\displaystyle \Rightarrow \log_ex\left(\frac{1}{\log_e10} + 1\right)= 3 - \log_e2$

Can you finish it from here?

Grandad