I don't if I'm right for these two questions i just need a check if I'm right,if I'm wrong please show me how to get that answer.

Rewrite the following exponential functions as logarithmic functions

a)f(x)=9^x

ans:f(x) Log^-1(xlog(9))

b)f(x)=(7/8)^x

ans:log^-1(x(log 7 - log 8)

i don't know if I'm right for the answer,so i just need to know and if I'm wrong prove please show me how to be right.

Yes, but count brackets. I try to use different ones

log^-1[ x(log 7 - log 8) ]

Okay i was wondering because some people told me the answer is log(f(x))=2xlog(3)

For a)

well

9^x = 3^(2x)
so log^-1 (2 x log 3)
is a perfectly good answer. So is Log^-1(xlog(9))

They are the same :)

So i guess my answer is acceptable right :)

I think your answer is fine. So is the 3^2 = 9 one.

To rewrite exponential functions as logarithmic functions, you need to understand the relationship between exponentiation and logarithms. The logarithm of a number tells you the exponent to which a given base must be raised to obtain that number.

a) Let's rewrite the exponential function f(x) = 9^x as a logarithmic function. To do this, we can use the base 9 logarithm. The logarithmic function that corresponds to f(x) = 9^x can be written as log9(f(x)) = x. In other words, the logarithm of f(x) with base 9 is equal to x.

So the correct answer should be f(x) = log9(x).

b) Now let's rewrite the exponential function f(x) = (7/8)^x as a logarithmic function. To do this, we can use the base (7/8) logarithm. The logarithmic function that corresponds to f(x) = (7/8)^x can be written as log(7/8)(f(x)) = x.

However, to simplify this further, we can use the property of logarithms that states log(a/b) is equal to log(a) - log(b). So, we can rewrite the expression as log(7) - log(8) = x.

Therefore, the correct answer should be f(x) = log(7) - log(8).