Question

if log x y is equals to 0.9 and log x upon Y is equals to 0.5 the value of log under root y is​

Answer 1

log(m*n) = log m + log n

log (xy) = log x + log y =0 .9

log(m/n) = log m - log n (eq 1)

so

log (x/y) = log x - log y = 0.5 (eq 2)

adding equation 1 and 2

log x + log y +log x - log y = 1.4

2 log x = 1.4

log x = 0.7

putting this in eq 2

log x - log y = 0.5

0.7 - log y = 0.5

log y = 0.7 - 0.5

log y = 0.2

log (√y) = log ( y^(1/2))

log (m^ n) = n log m

so

log √y = 1/2 * log y

putting value of log y

log √y = 1/2 * 0.2= 0.1

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Answer 2

Answer:

The correct answer is 0.1

Step-by-step explanation:

Given Data :

Log xy= 0.9

Logx/Logy = 0.5

Formula Used :

Log mn = log m + log n

Log (m/n) = log m - log n

Log ( m^n) = n log m

Obtaining Results :

Log xy = log x + log y = 0.9 ...... equation (1)

Log (x/y) = log x - log y = 0.5 ......equation (2)

Adding equation (1) and (2) , we get :

2Logx = 1.4

Logx = 0.7

Putting Logx = 0.7 in equation (1)

0.7 + log y = 0.9

log y = 0.9 - 0.7 = 0.2

Now,

log (√y ) = 1/2 log y

$log( \sqrt{y} ) = \frac{1}{2} \times 0.2 \\ log( \sqrt{y} ) = 0.1$

Hence, the required answer is 0.1

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