Answer: To find the two integers between which the solution to 4^x = 50 lies, we can take the logarithm base 4 of both sides of the equation: x = log4(50). The logarithm of 50 with base 4 is approximately 2.3219. Since the logarithm of a number is always positive, the solution to 4^x = 50 lies between 2 and 3.
To find the exact solution, we can change the equation to logarithmic form by taking the logarithm base 4 of both sides: log4(4^x) = log4(50)
Using the logarithmic identity: log(b^x) = x*log(b)
So we have: x*log(4) = log(50)
Dividing both sides by log(4), we have:
x = log(50) / log(4)
To find the exact solution we can approximate log(50) / log(4) using a calculator or logarithm tables. The exact solution is x ≈ 2.32192809488736218170856773213.
So, the exact solution is x = 2.32192809488736218170856773213, which is between 2 and 3, as stated before.
Explanation: