Answer to Question #261008 in Algebra for Master J

Question

If log_𝑎 𝑞 = 1/5 solve the equation , 𝑥 log_𝑎 𝑞 + (𝑥 + 2) log_𝑎 𝑞² = 3 

Answer 1

Given: log_𝑎 𝑞 = 1/5 ...(1)

Now, 𝑥 log_𝑎 𝑞 + (𝑥 + 2) log_𝑎 𝑞² = 3 

$\Rightarrow$ 𝑥 log_𝑎 𝑞 + (𝑥 + 2).(2 log_𝑎 q) = 3 [$\because log a^m = m. log a$ ]

$\Rightarrow$  $\frac{x}{5}+(x+2)\times2\times \frac 1 5=3$ [From eq. (1)]

$\Rightarrow x+2x+4=15\\ \Rightarrow 3x=11 \\\Rightarrow x =\frac {11}{3}$