Home
Class 12
MATHS
if log10 5=a and log10 3=b then:...

if `log_10 5=a` and `log_10 3=b` then:

A

` log_(30) 8 = (3(1-a))/(b+1) `

B

` log_(40)15= (a+b)/(3-2a)`

C

` log_(243) 32 = (1-a)/b`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A, B, C
(1) ` log_(30) 8 = (3log_(10)2)/(log_(10)5+log_(10) 3+log_(10)2)`
` = (3(1-log_(10)5))/(log_(10)5+log_(10)3+log_(10)2)`
` = (3(1-log_(10)5))/(1+log_(10)3) = (3(1-a))/(1+b)`
(2)` log_(40) 15=(log_(10)15)/(log_(10)40)`
` = (log_(10)3+log_(10)5)/(log_(10)5+3[1-log_(10)5])=(a+b)/(3-2a)`
(3) `log_(243)32 = (log_(10)2)/(log_(10)3)=(1-log_(10)5)/(log_(10)3) = (1-a)/b `
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise (Comprehension)|6 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise (Matrix)|3 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise (Single)|50 Videos

  • LOGARITHM AND ITS APPLICATIONS

    CENGAGE|Exercise Subjective Type|9 Videos

  • MATHMETICAL REASONING

    CENGAGE|Exercise JEE Previous Year|10 Videos

Similar Questions

Explore conceptually related problems

If (log)_(10)5=aand(log)_(10)3=b, then (A)(log)_(30)8=(3(1-a))/(b+1)(B)(log)_(40)15=(a+b)/(3-2a)(C)(log)_(243)32=(1-a)/(b) (d) none of these

If log_(10) 2 = a, log_(10)3 = b" then "log_(0.72)(9.6) in terms of a and b is equal to

If log_(10) a= p and log_(10) b = q, then what is log_(10) (a^(p)b^(q)) equal to ?

Given log_(10)2 = a and log_(10)3 = b . If 3^(x+2) = 45 , then the value of x in terms of a and b is-

if log_(10)x=a, log_(10)y=b and log_(10)z=c , then antilog (pa + qb - rc) =?

Given that log_10 2 =x, log_10 3 =y then log_10 1.2=

It is given that log_(10) 2 = 0·301 and log_10 (3) = 0·477. How many digits are there in : ((108))^(10) ?

If log_(10) 4 = 0.6021 and log_(10)5 = 0.6990, then find the value of log_(10) 1600.

If log_(10)x=a,log_(10)y=b" and "log_(10)z=c , then antilog (pa+qb-rc)=?