Answer:
you can determine the value of x that satisfies the exponential equation 4^(5x-2) = 7.
Step-by-step explanation:
1. **Isolate the Exponential Term:** Begin by isolating the exponential term on one side of the equation. In this case, we have 4^(5x-2) = 7.
2. **Convert 7 to a Power of 4:** Since the base on the left side of the equation is 4, we want to express 7 as a power of 4. In this case, 7 can be written as 4^(log4(7)), where log4 represents the logarithm base 4.
3. **Set Exponents Equal:** Once both sides of the equation have the same base (4 in this case), you can set the exponents equal to each other. This gives us the equation 5x-2 = log4(7).
4. **Solve for x:** Now, you can solve for x by isolating it on one side of the equation. Add 2 to both sides of the equation to get 5x = log4(7) + 2, then divide by 5 to find the value of x.
By following these steps, you can determine the value of x that satisfies the exponential equation 4^(5x-2) = 7.
