Question

2. Solve 5 power 3x+1 = 2 power 5x+2.
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Answer 1

Answer:

$\large\boxed{\sf{-\dfrac{9}{57}}}$

Step-by-step explanation:

${5}^{3x + 1} = {2}^{5x + 2}$

Taking log both sides, we get

$= > (3x + 1)log(5) = (5x + 2) log(2) \\ \\ = > \frac{ log(5) }{ log(2) } = \frac{5 x+ 2}{3x + 1} \\ \\ = > \frac{0.69}{0.30} = \frac{5x + 2}{3x + 1} \\ \\ = >( 3x + 1)0.69 = (5x + 2)0.30 \\ \\ = > 2.07 x+ 0.69 = 1.50x + 0.60 \\ \\ = > 2.07x - 1.50x = 0.60 - 0.69 \\ \\ = > 0.57x = - 0.09 \\ \\ = > x = - \frac{0.09}{0.57} \\ \\ = > x = - \frac{9}{57}$