We can solve this using logarithms.
Logarithms are written in the form [tex] \log_b(n) = p [\tex], where b is the base, n is the number, and p is the power.
In the problem, 4 is the base raise to the power of x. We can take the logarithm of both sides to solve for x.
[tex] \log_4(4^{x}) = log_4(19) [\tex]
The first half of this equation can be written as:
[tex] 4^{?} = 4^{x} [\tex]. The logarithm cancels out the 4, and we are left with:
[tex] x = \log_4(19) [\tex]
Note: The default base for logarithms is base 10, so to get a numerical answer, type log(19)/log(4) into a calculator. This is the change of base formula. You will get 2.12396.
