log4(2log3( 1 + log2( 1 + 3log3 x))) = 1/2 Find x - Maths - Relations and Functions

Question

log4(2log3( 1 + log2( 1 +
3log3 x))) = 1/2 Find x

Anuradha Sharma · Accepted Answer

Given,

log4(2log3(
1 + 
log2(
1 + 
3log3

x))) = 1/2
now we know that
, If logmn=k then n = mk using this property we can easily solve
the problem, log4(2log3(1+log2(1+3log3x))) = 1/2

(2log3(
1 + 
log2(
1 + 
3log3

x))) = 41/2 =2

2log3(
1 + 
log2(
1 + 
3log3

x)) = 2

log3(
1 + 
log2(
1 + 
3log3

x)) = 1

1 + 
log2(
1 + 
3log3

x) = 31 
log2(
1 + 
3log3

x) = 3-1= 2
1 + 
3log3

x = 22 
3log3

x = 4-1 = 3

log3

x =1 or x = 31 =3
x = 3
Answer

log4(2log3( 1 + log2( 1 + 3log3 x))) = 1/2. Find x.