If the sum of first 23 terms of the series log x3 - log x4y2 - log x5y4 - - can be expressed in the form of log xayb - then a - b equals-

The correct option is B 828 log x^3 + log (x^4y^2 ) + log (x^5y^4 ) + .... log (x^25y^44 ) = logx^3 + .... + 25y^2 + .... + 44= logx^322y^506 .Thus ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

nth Term of A.P

If the sum of...

Question

If the sum of first $23$ terms of the series $log x^{3} + log (\frac{x^{4}}{y^{2}}) + log (\frac{x^{5}}{y^{4}}) + . . . .$ can be expressed in the form of $log (\frac{x^{a}}{y b})$ , then $(a + b)$ equals.

805

No worries! We‘ve got your back. Try BYJU‘S free classes today!

828

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

851

No worries! We‘ve got your back. Try BYJU‘S free classes today!

854

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is B $828$
$log x^{3} + log (\frac{x^{4}}{y^{2}}) + log (\frac{x^{5}}{y^{4}}) + . . . . log (\frac{x^{25}}{y^{44}}) = log \frac{x^{3 + . . . . + 25}}{y^{2 + . . . . + 44}} = log \frac{x^{322}}{y^{506}}$ .
Thus $a + b = 322 + 506 = 828$ .

Suggest Corrections

Similar questions

Q. If

{log}_{x} 2 = a, {log}_{x} 3 = b, {log}_{x} 5 = c

then find the value of the following in terms of

a, b

and

c

(i)

{log}_{x} 16

(ii)

{log}_{x} 75

(iii)

{log}_{x} 60

Q. If

{log}_{x} 2 = a, {log}_{x} 3 = b, {log}_{x} 5 = c,

then find the value of the following in terms of a, b, and c,
(i)

{log}_{x} 16

(ii)

{log}_{x} 75

(iii)

{log}_{x} 60

Q. If

u = log (\frac{x^{4} + y^{4}}{x^{2} + y^{2}})

, then

x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y}

is equal to

Q. Let

A

be the sum of the first

20

terms and

B

be the sum of the first

40

terms of the series

1^{2} + {2.2}^{2} + 3^{2} + {2.4}^{2} + 5^{2} + {2.6}^{2} + . . . . .

B - 2 A = 100 λ

, then

λ

is equal to

Q. Let

A

be the sum of the first

20

terms and

B

be the sum of the first

40

terms of the series

1^{2} + 2 \cdot 2^{2} + 3^{2} + 2 \cdot 4^{2} + 5^{2} + 2 \cdot 6^{2} + \dots .

B - 2 A = 100 λ

, then

λ

is equal to

Join BYJU'S Learning Program

If the sum of first 23 terms of the series logx3+log(x4y2)+log(x5y4)+.... can be expressed in the form of log(xayb), then (a+b) equals.

The correct option is B 828logx3+log(x4y2)+log(x5y4)+....log(x25y44)=logx3+....+25y2+....+44=logx322y506.Thus a+b=322+506=828.

If the sum of first $23$ terms of the series $log x^{3} + log (\frac{x^{4}}{y^{2}}) + log (\frac{x^{5}}{y^{4}}) + . . . .$ can be expressed in the form of $log (\frac{x^{a}}{y b})$ , then $(a + b)$ equals.

The correct option is B $828$
$log x^{3} + log (\frac{x^{4}}{y^{2}}) + log (\frac{x^{5}}{y^{4}}) + . . . . log (\frac{x^{25}}{y^{44}}) = log \frac{x^{3 + . . . . + 25}}{y^{2 + . . . . + 44}} = log \frac{x^{322}}{y^{506}}$ .
Thus $a + b = 322 + 506 = 828$ .