Question

the value of y in logy1369y=3​

Answer 1

Answer:

37

Explanation:

logy 1369y=3

logy 1369+logy y=3

logy 37^2 +1=3

2 logy 37=2

logy 37=2/2

log37/log y=1

log 37=log y

Answer 2

The value of Y is 37 in $log_y$ 1369 y = 3

Explanation:

Given Data

$log_y$ 1369 y = 3

Apply the log rule $log_a$b = ln (b) ÷ ln (a)

$log_y$ 1369 y = ln (1369 y) ÷ ln (y)

ln(1369) ÷ ln (y) =3

Multiply both sides by ln(y)

[ln(1369) ÷ ln (y)] × ln(y) = 3 ln(y)

ln(y) is cancelled on left side

ln(1369) = 3 ln(y) --------> 1

Apply the log rule

$log_c$ (ab) = $log_c$(a) + $log_c$ (b)

ln (1369y) = ln(1369) + ln(y) ----------> 2

Substitute 2 in 1

ln (1369) + ln (y) = 3 ln(y)

Subtract ln (1369) on both sides

ln (1369) + ln (y) - ln (1369) = 3 ln(y) - ln (1369)

ln (y)  = 3 ln(y) - ln (1369)

Subtract 3 ln(y)  on both sides

ln (y) - 3 ln(y) = 3 ln(y) - ln (1369) - 3 ln(y)

-2 ln (y) = - ln (1369)

Eliminate negative signs on both sides

2 ln (y) =  ln (1369)

Divide by 2 on  both sides

2 ln (y) ÷ 2 =  ln (1369) ÷ 2

ln (y) =  ln (1369) ÷ 2

where 1369 = (37)²

ln (y) = ln (37)² ÷ 2

ln (37)²  can be written as 2 ln (37)

ln (y) = 2 ln (37) ÷ 2

ln (y) = ln (37)

Remove log on both sides

y = 37

Therefore the value of y in $log_y$ 1369 y = 3 is 37

To learn more ...

1.  https://brainly.in/question/4383672

2.  https://brainly.in/question/9850753