Question

Solve the following equations.
${3.4}^x+\frac{1}{3}\cdot 9^{x+2}={6.4}^{x+1}-\frac{1}{2}\cdot 9^{x+1}$

Answer 1

${3.4}^x+\frac{1}{3}\cdot 9^{x+2}={6.4}^{x+1}-\frac{1}{2}\cdot 9^{x+1}$

$\Rightarrow {3.4}^x+\frac{1}{3}\cdot 9^x\cdot 9^2={6.4}^x\cdot 4-\frac{1}{2}{9}^x\cdot 9$

$\Rightarrow {3.4}^x-{24.4}^x=\frac{-81}{3}\cdot 9^x-\frac{9}{2}\cdot 9^x$

$\Rightarrow 4^x(3-24)=-9^x(27+\frac{9}{2})$

$\Rightarrow 4^x(-21)=-9^x\cdot \frac{63}{2}$

$\Rightarrow \frac{4^x}{9^x}=\frac{63}{2}\times \frac{1}{21}$

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

$\Rightarrow {\left(\frac{2}{3}\right)}^{2x}={\left(\frac{2}{3}\right)}^{-1}$

$\Rightarrow 2x=7$

$x=-\frac{1}{2}$ Solved