SOLUTION: Please help me with these questions ASAP!! Suppose that f(x)=log3(x-1) a)If f(6)=1.4 and f(8)=1.7,then evaluate log3(35) and log3(7/5). b)If f(3)=0.6, find log9(2).

Question 276590: Please help me with these questions ASAP!!
Suppose that f(x)=log3(x-1)
a)If f(6)=1.4 and f(8)=1.7,then evaluate log3(35) and log3(7/5).
b)If f(3)=0.6, find log9(2).
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

We're told that f(6) = 1.4 so

We're told that f(8) = 1.4 so
a)
Since the only base 3 logs we know are and , we need to express in terms of the other two. Since 35 = 7*5 we can start with

This does not mean that . But we can use a property of logarithms, , to separate our log into two separate logs:

For we'll use another property of logarithms:

b)
Since we're told that f(3) = 0.6, .
For we do not know any base 9 logs and 2 is not an obvious power of 9. So what so we do? Well we do know several base 3 logarithms so we'll use the base conversion formula formula, , to change this base 9 logarithm into an expression of base 3 logarithms:

From above we know the numerator and the denominator can be done "by hand" since 9 is a well known power of 3:

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