A) 243
B) 27
C) 343
D) 64
Correct Answer: C
Solution :
Changing the base, |
\[\frac{\log (lo{{g}_{2}}x)}{\log 3}+2\frac{\log (lo{{g}_{7}}8)}{\log 9}=2\] |
\[\frac{\log (lo{{g}_{2}}x)}{\log 3}+2\frac{\log (lo{{g}_{7}}8)}{2\log 3}=2\]\[\Rightarrow \]\[\log ({{\log }_{2}}x)+\log ({{\log }_{7}}8)=2\log 3\] |
\[\log ({{\log }_{2}}x\times {{\log }_{7}}8)=\log 9\Rightarrow {{\log }_{2}}x\times {{\log }_{7}}8=9\] |
\[\Rightarrow \frac{3\log x}{\log 7}=9\] |
\[\log x=3\log 7\Rightarrow \log x=\log {{7}^{3}}\]\[\Rightarrow \,\,x=343.\] |
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