Home
Class 9
MATHS
If log(3)2=x then the value of (log(10)7...

If `log_(3)2=x` then the value of `(log_(10)72)/(log_(10)24)` is

A

`(1+x)/(1-x)`

B

`(2+3x)/(1+3x)`

C

`(2-3x)/(2+3x)`

D

Undefined

Text Solution

Verified by Experts

The correct Answer is:
B
Given , `log_(3)2=x`
`(log_(10)72)/(log_(10)24)= log_(24) 72 = log_(24) (24xx3)`
`= log_(24) + log_(24) 72 = log_(24) (24 xx 3)`
`= log_(24) 24 + log _(24) 3 = 1 + (log3)/(log24)`
`1+ (log_(3)3)/(log_(3)24)`
` 1+ 1/ (log_(3)3 + log_(3)8)`
` 1+ 1/ ( 1+ log_(3) 2^(3))`
`= ( 1+3 log _(3)2+1)/(1+3log_(3)2)= (2+3x)/(1+3x)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the value of log_(10)5*log_(10)20+(log_(10)2)^(2)

Positive numbers x,y backslash and backslash z satisfy xyz:)=(:10^(1) and (log_(10)x)*(log_(10)yz)+(log_(10)y)*(log_(10)z)=468. Find the value of (log_(10)x)^(2)+(log_(10)y)^(2)+(log_(10)z)^(2)

Positive numbers x,y and z satisfy xyz=10^(81) and (log_(10)x)(log_(10)yz)+(log_(10)y)(log_(10)z)=468. Find the value of (log_(10)x)^(2)+(log_(10)y)^(2)+(log_(10)z)^(2)

The value of (3 + log_(10) (10)^(2))/(log_(5)5) is _______

If log_(10)(sin(x+pi/4))=(log_(10)6-1)/2 , the value of log_(10)(sinx)+log_(10)(cosx) is

log_(10)3+log_(10)2-2log_(10)5

If the positive numbers x,y&z satisfy xyz=1000,log_(10)x log_(10)y+log_(10)xy log_(10)z=1 and log_(x)10+log_(y)10+log_(z)10=(1)/(3) then the value of root(3)((log_(10)x)^(3)+(log_(10)y)^(3)+(log_(10)z)^(3)) is

Givenlog (2)=0.3010 and log_(10)(3)=0.4771 find the value of 7log_(10)((10)/(9))-2log_(10)((25)/(24))+3log_(10)((81)/(80))