Write the exponential function f(x)=4^x-3 in the form f(x)=ab^x
4^(x-3) = 4^x/4^3 = 1/64 * 4^x
do you mean
f(x) = 4^(x-3) ???
that is 4^x / 4^3
= 4^x /64
= (1/64) 4^x
Thank yβall for explaining it ! :-) now I know how to do this kind of question !
To write the exponential function f(x) = 4^x - 3 in the form f(x) = ab^x, we need to express the base, 4, as a different base, b.
To do this, we can use logarithms. Specifically, we'll use the logarithm with base b, denoted as log(base b).
Starting with the original function:
f(x) = 4^x - 3
Take the logarithm of both sides with base 4:
log(base 4)(f(x)) = log(base 4)(4^x - 3)
Now, let's apply the logarithmic property that states log(base b)(b^x) = x:
log(base 4)(f(x)) = x * log(base 4)(4) - log(base 4)(3)
Since log(base 4)(4) equals 1, we have:
log(base 4)(f(x)) = x - log(base 4)(3)
Now, to bring f(x) back to the form f(x) = ab^x, we can rewrite it using exponential form:
f(x) = 4^(x - log(base 4)(3))
So, in the form f(x) = ab^x, the function f(x) = 4^x - 3 can be written as f(x) = 4^(x - log(base 4)(3)).