suppose f(x)=logaX and f(3)=2 determine each function value a) f(1/9) b)f(27) c)

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From what is given means that: a^(f(x))= x. We have a^f(3) = x ------> a^2=3. --------> a= square root of 3. Te answer is plus minus square root of 3 but we need only the positive value. Answer a). Log (1/9) base square root 3. It will be (sqrt3)^x =1/9 or (sqrt3)^x = 9^(-1). 9 is (sqrt3)^4. we have (sqrt3)^k= (sqrt3)^(-4) therefore k =-4. This the value of f(1/9)=-4. b).log 27 base (sqrt3). (sqrt3)^m = 27 this is from the definition of logarithm. also 27 = 3^3 = (sqrt3)^6 we have (sqrt3)^m= sqrt^6 so m=6 which will be f(27)=6. c).log9 base (sqrt3). We have (sqrt3)^n = 9. 9 is also (sqrt3)^4. (sqrt3)^n= (sqrt3)^4 so n= 4 and therefore f(9)=4.

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