1. Tardigrade
  2. Question
  3. Mathematics
  4. Find the value of x satisfying the equation (1/ log 6(x+3))+(2 log 0.25(4-x)/ log 0.5(x+3))=0.

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. Find the value of $x$ satisfying the equation $\frac{1}{\log _6(x+3)}+\frac{2 \log _{0.25}(4-x)}{\log _{0.5}(x+3)}=0$.

Continuity and Differentiability

Solution:

$\log _{x+3} 6-\log _{x+3}(x+3)+\frac{2 \log _{0.5}(4-x)}{\left(\log _{0.5} 0.25\right) \log _{0.5}(x+3)}=0$
$\log _{x+3}\left(\frac{6}{x+3}\right)+\frac{\log _{0.5}(4-x)}{\log _{0.5}(x+3)}=0 $
$\Rightarrow \log _{x+3}\left(\frac{6}{x+3}\right)+\log _{x+3}(4-x)=0$
$\Rightarrow \log _{x+3}\left(\frac{6(4-x)}{x+3}\right)=0 \Rightarrow \frac{6(4-x)}{x+3}=1 $
$\Rightarrow 24-6 x=x+3 \Rightarrow 7 x=21 \Rightarrow x=3$