Question

Solve the following equations, having given $\log 2,\log 3$, and $\log 7$.
${21}^x=2^{2x+1}.5^x$.

Answer 1

${21}^x=2^{2x+1}\times 5^x$

Taking logarithm on both sides,

$\Rightarrow x\log 21=(2x+1)\log 2+x\log 5$

$\Rightarrow x\log 3+x\log 7=(2x+1)\log 2+x(1-\log 2)$

$\Rightarrow x\log 3+x\log 7=(x+1)\log 2+x$

$\Rightarrow (\log 3+\log 7-\log 2-1)x=\log 2$

$\Rightarrow x=\frac{\log 2}{\log 3+\log 7-\log 2-1}$