Question

What is the solution to the equation log 4(x) = 7?

Answer 1

The equation log 4(x) = 7 is solved by rewriting it in exponential form as x = 4^7, which calculates to x = 16,384. This illustrates the inverse relationship between logarithmic and exponential functions.

Step-by-step explanation:

The solution to the equation log 4(x) = 7 involves understanding the properties of logarithms and exponentiation. In this case, the logarithm indicates that the power to which the number 4 must be raised to get x is 7. To find x, we can use the inverse of the logarithmic function, which is the exponential function.

Step-by-Step Solution

1. 
   
3. Write the equation in exponential form: 4^7 = x.
4. 
   
6. Calculate 4 raised to the power of 7: 4^7 = 16,384.
7. 
   
9. Substitute the computed value as x: x = 16,384.

Therefore, the solution to the equation log 4(x) = 7 is x = 16,384.