Question

If ${\log }_{2}x+{\log }_{4}x+{\log }_{64}x=5$, then $x=$.......

• A. $8$
• B. $16$
• C. $7$
• D. $2$

Answer 1

The correct option is A $8$

${\log }_{2}x+{\log }_{4}x+{\log }_{64}x=5$

$\Rightarrow$ $\frac{\log x}{\log 2}+\frac{\log x}{\log 4}+\frac{\log x}{\log 64}=5$

$\Rightarrow$$\frac{\log x}{\log 2}+\frac{\log x}{2\log 2}+\frac{\log x}{6\log 2}=5$

$\Rightarrow$$\frac{6\log x+3\log x+\log x}{6\log 2}=5$

$\Rightarrow$$\frac{10\log x}{6\log 2}=5$

$\Rightarrow$$\frac{10\log x}{\log 2}=30$

$\Rightarrow$$\frac{\log x}{\log 2}=3$

$\Rightarrow$$\log x=3\log 2$

$\Rightarrow$$\log x=\log 2^3$

$\Rightarrow$$x=8$