To solve this equation, we can start by simplifying the left side:

(2³x - 7) * 7¹⁰ = 7¹²

Using the exponent rule for multiplication, we can rewrite 7¹⁰ as (7²)⁵:

(2³x - 7) * (7²)⁵ = 7¹²

Simplifying further, we have:

(2³x - 7) * 7¹⁰ = 7¹²

(2³x - 7) * 49 = 7¹²

Now, we can distribute the 49 to both terms inside the parentheses:

49 * 2³x - 49 * 7 = 7¹²

98³x - 343 = 7¹²

Next, we can add 343 to both sides of the equation:

98³x - 343 + 343 = 7¹² + 343

98³x = 7¹² + 343

Now, we can subtract 343 from both sides:

98³x = 7¹² + 343 - 343

98³x = 7¹²

Finally, we can divide both sides by 98³ to solve for x:

x = 7¹² / 98³

x = 7¹² / (98³)

x = 7¹² / 941,192

Therefore, the solution to the equation is x = 7¹² / 941,192.