# SOLUTION: If (log_9)4=a and (log_27)5=b, find and expression in terms of a and b for log_(square root over 3)40

Algebra ->  Algebra  -> Polynomials-and-rational-expressions -> SOLUTION: If (log_9)4=a and (log_27)5=b, find and expression in terms of a and b for log_(square root over 3)40      Log On

 Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help! Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

 Algebra: Polynomials, rational expressions and equations Solvers Lessons Answers archive Quiz In Depth

 Click here to see ALL problems on Polynomials-and-rational-expressions Question 177206: If (log_9)4=a and (log_27)5=b, find and expression in terms of a and b for log_(square root over 3)40Answer by stanbon(57967)   (Show Source): You can put this solution on YOUR website!If (log_9)4=a So 9^a = 4 Therefore (sqrt(3))^(4a) = 4 And log(sqrt(3)4 = 4a Also log(sqrt(3)2 = 2a --------------------------------- and (log_27)5=b So 27^b = 5 Therefore (sqrt(3))^(6b) = 5 And log(sqrt(3)5 = 6b ----------------------------------- find and expression in terms of a and b for log_(square root over 3)40 log(sqrt(3))40 = log(sqrt(3)[2*4*5] log(sqrt(3))2 + log(sqrt(3)4 + log(sqrt(3)5 = 2a + 4a + 6b = 6(a+b) ============== Cheers, Stan H.