Home
Class 12
MATHS
Suppose that a and b are positive real n...

Suppose that a and b are positive real numbers such that `log_(27)a+log_9(b)=7/2` and `log_(27)b+log_9a=2/3`.Then the value of the `ab` equals

Text Solution

Verified by Experts

`log_(27)a+log_(9)b= 7/2 and log_(27)b+log_(9) a = 2/3`
` rArr 1/3 log _(3) a + 1/2 log _(3) b= 7/2`
` and 1/3 log_(3) b+1/2 log _(3) a = 2/3`
Adding the equations, we get
`1/3 log_(3)(ab)+1/2 log_(3)(ab) = 7/2+2/3 = 25/6`
` or 5/6 log_(3) (ab) = 25/6`
`or log_(3) (ab) = 5 `
` or ab = 3^(5) = 243`
Promotional Banner

Topper's Solved these Questions

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.1|6 Videos

  • LOGARITHM AND ITS PROPERTIES

    CENGAGE|Exercise Exercise 1.2|9 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

Suppose that a and b are positive real numbers such that log_(27)a+log_(9)(b)=(7)/(2) and log_(27)b+log_(9)a=(2)/(3). Then the value of the ab equals

Suppose that a and b are positive real numbers such that log_(27) a + log_(9) b = 7/2 " and " log_(27) b + log_(9) a = 2/3 . Find the value of the ab.

If a, b, c, are positive real numbers and log_(4) a=log_(6)b=log_(9) (a+b) , then b/a equals

Evaluate: log_(9)27 - log_(27)9

If log_(a)b=2,log_(b)c=2, and log_(3)c=3+log_(3)a then the value of c/(ab) is..........

Let B,C,P and L be positive real numbers such that log(B*L)+log(B*P)=2;log(P*L)+log(P*C)=3;log(C*B)+log(C*L)=4 The value of the product (BCPL) equals (base of the log is 10)

If log_(a)b=2, log_(b)c=2, and log_(3) c= 3 + log_(3) a,then the value of c/(ab)is ________.

If log27=1.431, then the value of log 9 is

if a,b,c are positive real numbers such that a^(log_(3)7)=27;b^(log711)=49 and c^(log_(11)25)=sqrt(11) then the value of {a^(log_(3)7)sim2+b^(log_(7)11)^^2+c^(log_(11)25)^^2} is

If log_(4)A=log_(6)B=log_(9)(A+B) then the value of (B)/(A) is