36^log 4 to the base 6
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Answered by
17
Hi ,
We know laws of logarithm:
********!***********************************
1.) log a ( a ) = 1
2) log a ( x^n) = n × log a ( x )
******************************************
Let x = 36 ^ [ log 6 ( 4 ) ]
Take log bothsides
log 6 ( x ) = log { 36 ^[ log 6 (4) ] }
log 6 ( x ) = [ log 6 (4) ] × [ log 6 ( 36 ) ]
log 6 ( x ) = [ log 6 ( 4 ) ] × [ log6( 6^2 )]
log 6 ( x ) = [ log 6 (4)] × [2× log 6(6) ]
log 6( x ) = [ log 6 (4) ] × 2
log 6 ( x ) = 2 × log 6 ( 4 )
log 6 ( x ) = log 6 ( 4 ^2 )
Remove log bothsides
x = 4 ^2
x = 16
I hope this will useful to you.
****
We know laws of logarithm:
********!***********************************
1.) log a ( a ) = 1
2) log a ( x^n) = n × log a ( x )
******************************************
Let x = 36 ^ [ log 6 ( 4 ) ]
Take log bothsides
log 6 ( x ) = log { 36 ^[ log 6 (4) ] }
log 6 ( x ) = [ log 6 (4) ] × [ log 6 ( 36 ) ]
log 6 ( x ) = [ log 6 ( 4 ) ] × [ log6( 6^2 )]
log 6 ( x ) = [ log 6 (4)] × [2× log 6(6) ]
log 6( x ) = [ log 6 (4) ] × 2
log 6 ( x ) = 2 × log 6 ( 4 )
log 6 ( x ) = log 6 ( 4 ^2 )
Remove log bothsides
x = 4 ^2
x = 16
I hope this will useful to you.
****
Answered by
0
Answer:
x = 16
Step-by-step explanation:
Let x = 36 ^ [ log 6 ( 4 ) ]
Take log both sides
log 6 ( x ) = log { 36 ^[ log 6 (4) ] }
log 6 ( x ) = [ log 6 (4) ] × [ log 6 ( 36 ) ]
log 6 ( x ) = [ log 6 ( 4 ) ] × [ log6( 6^2 )]
log 6 ( x ) = [ log 6 (4)] × [2× log 6(6) ]
log 6( x ) = [ log 6 (4) ] × 2
log 6 ( x ) = 2 × log 6 ( 4 )
log 6 ( x ) = log 6 ( 4 ^2 )
Remove log both sides
x = 4 ^2
x = 16
HOPE THIS WILL HELP ...
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