Question

Solve 5^x-4 = 7 for x using the change of base formula logb y = log y/ log b. Choose the correct value:

5.209
4.827
-2.791
-3.173

Answer 1

To solve the equation 5^x-4 = 7 using the change of base formula logb y = log y / log b, we rewrite the equation as log 5 (7) = x - 4. By applying the change of base formula, we find that x is approximately 4.827.

Step-by-step explanation:

To solve the equation 5^x-4 = 7 using the change of base formula logb y = log y / log b, we can rewrite the equation as log 5 (7) = x - 4.

Using the change of base formula, we have log 7 / log 5 = x - 4.

Adding 4 to both sides, we get x = log 7 / log 5 + 4. Evaluating this expression, we find that x is approximately 4.827. Therefore, the correct value is 4.827.