Question

if log 2 =x,log3=y and log7=z express log(4(63)1^2 ) in yerms of x,y andz

Answer 1

log 2 = x,
log 3 = y,
log 7 = z
Then,
$log(4 \times \sqrt{63} )$
$log(4) \: + \: log( \sqrt{63} )$

$log( {2}^{2} ) \: + \: log( {63}^{ \frac{1}{2} } )$
$2 \times log(2) \: + \: \frac{1}{2} \times log(63)$
$2 \: \times \: log(2) \: + \: log(9 \times 7)$
$2(x)\: + \: log(9) \: + \: log(7)$
$2x \: + \: log( {3}^{2} ) \: + \: log(7)$
$2x \: + \: 2 log(3) \: + \: log(7)$
$2x \: + \: 2y \: + \: z$

Answer 2

Answer:

2 x + 1/2 z + y

Step-by-step explanation:

log 2 = x

log 3 = y

log 7 = z

log ( 4 (63)^1/2 )

==> log ( 2² × √63 )

==> log 2² + log √63

==> 2 log 2 + log 63^(1/2)

==> 2 log 2 + 1/2 log 63

==> 2 log 2 + 1/2 log ( 7 × 9 )

==> 2 log 2 + 1/2 log 7 + 1/2 log 9

==> 2 x + 1/2 z + 1/2 log 3²

==> 2 x + 1/2 z + 1/2×2 log 3²

==> 2 x + 1/2 z + log 3

==> 2 x + 1/2 z + y

Hope it helps:)

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