110k views
4 votes
NO LINKS!!

44. Between which two integers would the solution to 4^x = 50 lie? Second, find the exact solution by changing to logarithmic form and solving.

1 Answer

0 votes

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:

User Cheresse
by
7.2k points