8-log-12x-1-4-log-27-solve-for-x-

Question Number 1355 by Rasheed Ahmad last updated on 25/Jul/15

8^{l o g (12 x + 1)} = 4^{l o g 27}, s o l v e f o r x .

Answered by Yugi last updated on 25/Jul/15

R e w r i t i n g t h e a b o v e e q u a t i o n i n b a s e 2 g i v e s

2^{3 l o g (12 x + 1)} = 2^{2 l o g 27} \dots \dots \dots . (1)

S i n c e t h e b a s e s a r e t h e s a m e, w e c a n e q u a t e

t h e i n d i c e s o n b o t h s i d e s o f (1) .

∴ 3 l o g (12 x + 1) = 2 l o g 3^{3}

3 l o g (12 x + 1) = 6 l o g 3

\div 3 : l o g (12 x + 1) = l o g 9

H e n c e 10^{l o g (12 x + 1)} = 10^{l o g 9}

∴ 12 x + 1 = 9 \Rightarrow x = \frac{2}{3}

Commented by Rasheed Soomro last updated on 25/Jul/15

T h a n k s . A p p r e c i a t i o n f o r y o u r a p p r o a c h .