If 2x^(log(4)3)+3^(log(4)x)= 27, then x ...

If `2x^(log_(4)3)+3^(log_(4)x)= 27`, then x is equal to

Text Solution

Verified by Experts

The correct Answer is:

` 2 x^(log_(4)3)+3^(log_(4)x) = 27`
` rArr 2 xx 3^(log_(4) x) + 3 ^(log_(4)x)+3^(log_(4)x) = 27`
` rArr 3^(log_(4)x) = 9 = 3^(2)`
` rArr log_(4) x = 2`
` :. X = 4^(2) = 16`.

Topper's Solved these Questions

LOGARITHM AND ITS PROPERTIES
CENGAGE ENGLISH|Exercise Multiple Correct Answers Type|18 Videos
LOGARITHM AND ITS PROPERTIES
CENGAGE ENGLISH|Exercise Linked Comprehension Type|6 Videos
LOGARITHM AND ITS PROPERTIES
CENGAGE ENGLISH|Exercise Exercise 1.6|6 Videos
LOGARITHM AND ITS APPLICATIONS
CENGAGE ENGLISH|Exercise Subjective Type|9 Videos
MATHMETICAL REASONING
CENGAGE ENGLISH|Exercise Archives|10 Videos

Similar Questions

Explore conceptually related problems

If 2x^((log)_4 3)+3^((log)_4x)=27 , then x is equal to

4^(log_9 3)+9^(log_2 4)=1 0^(log_x 83) , then x is equal to

If 3^(x+1)=6^(log_(2)3) , then x is equal to

If "log"_(3) a xx "log"_(a) x = 4 , then x is equal to

If (log)_3{5+4(log)_3(x-1)}=2, then x is equal to 4 (b) 3 (c) 8 (d) (log)_2 16

If log_(2)(log_(2)(log_(3)x))=log_(3)(log_(3)(log_(2)y))=0 , then x-y is equal to :

Match the column Column I, Column II If x=3,t h e n(log)_4(2(log)_3(1+(log)_2(1+3Log_3x))) is equal to, p. 3 If x=100 , then 3^((log)_3logsqrt(x))-logx+log^2x is equal to, q. 1 If one of the root of the equation 2((log)_xsqrt(5))^2-3(log)_x(a)+1=0 is sqrt(5) , then the other root is, r. 1/2 If (log)_2(4. 3^x-6)-(log)_2(9^x-6)=1, then x is equal to, s. 5

If log_(sqrt(2)) sqrt(x) +log_(2)(x) + log_(4) (x^(2)) + log_(8)(x^(3)) + log_(16)(x^(4)) = 40 then x is equal to-

If "log"_(x) (4x^("log"_(5)x) + 5) = 2 "log"_(5)x , then x equals to

CENGAGE ENGLISH-LOGARITHM AND ITS PROPERTIES-Exercises (Single Correct Answer Type)

If (log)(10)[1/(2^x+x-1)]=x[(log)(10)5-1] , then x= 4 (b) 3 (c) 2 ...
Text Solution
|
If (log)3{5+4(log)3(x-1)}=2, then x is equal to 4 (b) 3 (c) 8 (d) (...
Text Solution
|
If 2x^(log(4)3)+3^(log(4)x)= 27, then x is equal to
Text Solution
|
The equation log4(2-x)+log(0.25)(2+x)=log4(1-x)+log(0.25)(2x+1) has
Text Solution
|
The values of b for which the equation 2log(1/25)(bx+28)=1log5(12-4x-x...
Text Solution
|
If the equation 2^x(1-2^x)+4^y=2^y is solved for y in terms of x where...
Text Solution
|
The number of solution of x^(log(x)(x+3)^(2)) = 16is
Text Solution
|
The product of roots of the equation (log(8)(8//x^(2)))/((log(8)x)^(2)...
Text Solution
|
Let agt1 be a real number . If S is the set of real number x that are...
Text Solution
|
the number of roots of the equation log(3sqrtx) x + log(3x) (sqrtx) =0...
Text Solution
|
The set of all x satisfying the equation x^(log)3x^2+((log)3x)^(2-10)=...
Text Solution
|
Number of real values of x satisfying the equation (log)2(x^2-x)(log)...
Text Solution
|
If xy^(2) = 4 and log(3) (log(2) x) + log(1//3) (log(1//2) y)=1 , then...
Text Solution
|
If x1a n dx2 are the roots of the equation e^2 x^(lnx)=x^3 with x1> x2...
Text Solution
|
The number of real values of the parameter k for which (log(16)x)^2-(l...
Text Solution
|
x^((log)5x)>5 implies x in (0,oo) (b) (0,1/5)U(5,∞) (c) (2,2.5) (d)...
Text Solution
|
If S={x in N :2+(log)2sqrt(x+1)>1-(log)(1/2)sqrt(4-x^2)} , then (a)S...
Text Solution
|
If S={x in R :((log)(0. 6)0. 216)(log)5(5-2x)lt=0}, then S is equal t...
Text Solution
|
The solution set of inequality (1)/(2^(x)-1) gt (1)/(1-2^(x-1)) is
Text Solution
|
if log2 x+ log2 y >= 6 then the least value of x+y
Text Solution
|