Related InterviewSolutions

• if a,b,c are positive real numbers such that `a^(log_3(7));b^(log_7(11))=49 and c^(log_11(25))=sqrt(11)` find the vale of `a^((log_3(7))^2)+b^((log_7(11))^2)+c^((log_11(25))^2)`
• Find the values of `theta`, for which `cos3theta + sin3theta + (2sin2theta-3)(sintheta-costheta)` is always positive.
• Express the following in logarithimic form: a) `81 = 3^(4)` b) `0.001 = 10^(-3)` c) `2=128^(1//7)`
• Solve the system of equations: `(log)_a x(log)_a(x y z)=48(log)_a y log_a(x y z)=12 , a >0, a!=1(log)_a z log_a(x y z)=84 `
• Findthe product of the positive roots of the equation `sqrt((2008))(x)^((log)_(2008)x)=x^2dot`
• Find the value of `2log2/5 +3 log25/8 -log 625/128`
• Let `(x_0, y_0)`be the solution of the following equations:`(2x)^(1n2)=(3y)^(1n3)``3^(1nx)=2^(1ny)`The `x_0`is`1/6`(b) `1/3`(c) `1/2`(d) 6A. `1/6`B. `1/3`C. `1/2`D. 6
• The value of `cos^2 10^0-cos10^0cos50^0+cos^2 50^0`is equal to`4/3`(b) `1/3`(c) `3/4`(d) `3`A. `3/2(1+cos20^(@))`B. `3/4`C. `3/4+cos20^(@)`D. `63/16`
• If ` sin2A= lambda sin 2B` prove that `(tan(A+B)/tan(A-B))=(lambda+1)/(lambda-1)`
• The value of sin 10.sin 30. sin 50.sin 70 isA. `1/36`B. `1/32`C. `1/18`D. `1/16`