find-the-value-of-x-a-4-2x-1-5-x-2-6-1-x-b-4-3-2x-1-17-3-x-7-0-

Question Number 9753 by j.masanja06@gmail.com last updated on 31/Dec/16

f i n d t h e v a l u e o f x

(a) 4^{2 x + 1} . 5^{x - 2} = 6^{1 - x}

(b) 4 (3^{2 x + 1}) + 17 (3^{x}) - 7 = 0

Commented by ridwan balatif last updated on 31/Dec/16

(b) 4 (3^{2 x + 1}) + 17 (3^{x}) - 7 = 0

4 (3^{2 x} \times 3) + 17 (3^{x}) - 7 = 0

12 {(3^{x})}^{2} + 17 (3^{x}) - 7 = 0

let 3^{x} = a, then

{12 a}^{2} + 17 a - 7 = 0

(3 a - 1) (4 a + 7) = 0

a = \frac{1}{3} a = \frac{- 7}{4}

3^{x} = 3^{- 1} 3^{x} = \frac{- 7}{4} (IMPOSSIBLE)

x = - 1

Commented by ridwan balatif last updated on 31/Dec/16

(a) 4^{2 x + 1} . 5^{x - 2} = 6^{1 - x}

4^{2 x} \times 4 \times 5^{x} \times \frac{1}{25} = \frac{6}{6^{x}}

16^{x} \times \frac{2}{75} \times 5^{x} = \frac{1}{6^{x}}

480^{x} = \frac{75}{2}

\log (480^{x}) = \log (\frac{75}{2})

x . \log 480 = \log (\frac{75}{2})

x = \log_{480} (\frac{75}{2})

x \approx 0.587