solve-x-6-2x-4-3-3x-2-x-8-

Question Number 5902 by Ashis last updated on 04/Jun/16

s o l v e x

6^{2 x + 4} = 3^{3 x} 2^{x + 8}

Commented by prakash jain last updated on 04/Jun/16

6^{2 x} 6^{4} = 3^{3 x} 2^{x} 2^{8}

{(2 \cdot 3)}^{2 x} 3^{4} 2^{4} = 3^{3 x} 2^{x} 2^{8}

2^{2 x} 3^{2 x} 3^{4} 2^{4} = 3^{3 x} 2^{x} 2^{8}

\frac{2^{2 x} 3^{2 x}}{3^{3 x} 2^{x}} = \frac{2^{8}}{3^{4} 2^{4}}

\frac{2^{x}}{3^{x}} = \frac{2^{4}}{3^{4}}

{(\frac{2}{3})}^{x} = {(\frac{2}{3})}^{4}

x = 4

Answered by sanusihammed last updated on 04/Jun/16

S o l u t i o n

6^{2 x + 4} = 3^{3 x} 2^{x + 8}

T a k e t h e l o g a r i t h m o f b o t h s i d e s

l o g 6^{2 x + 4} = l o g (3^{3 x} 2^{x + 8})

(2 x + 4) l o g 6 = l o g 3^{3 x} + l o g 2^{x + 8}

(2 x + 4) l o g 6 = 3 x l o g 3 + (x + 8) l o g 2

(2 x + 4) 0.7782 = 3 x (0.4771) + (x + 8) (0.3010)

1.5564 x + 3.1128 = 1.4313 x + 0.3010 x + 2.408

1.5564 x + 3.1128 = 1.7323 x + 2.408

c o l l e c t t h e l i k e t e r m s

1.7323 x - 1.5564 x = 3.1128 - 2.408

0.1759 x = 0.7048

x = \frac{0.7048}{0.1759}

x = 4.0068

A p p r o x i m a t e l y

x = 4