Question

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

Answer 1

$5^{5-3x}=2^{x+2}$

Taking logarithm on both sides,

$\Rightarrow (5-3x)\log 5=(x+2)\log 2$

$\Rightarrow (5-3x)(1-\log 2)=(x+2)\log 2$

$\Rightarrow (5-3x)=(x+2)\log 2+(5-3x)\log 2$

$\Rightarrow (5-3x)=(7-2x)\log 2$

$\Rightarrow (2\log 2-3)x=(7\log 2-5)$

$\Rightarrow x=\frac{7\log 2-5}{2\log 2-3}$