To solve this equation, we need to first rewrite it in terms of powers of 2 and 4:
216^x - 32^4x - 1 + 7*4^2x - 1 = 120
Since 16 = 2^4 and 4 = 2^2, we can rewrite the equation as:
22^(4x) - 32^(4x) - 1 + 7(2^2)^(2x) - 1 = 12022^(4x) - 32^(4x) - 1 + 72^(4x) - 1 = 12022^(4x) - 32^(4x) + 72^(4x) - 2 = 12062^(4x) - 2 = 1206*16^x - 2 = 120
Next, we can isolate the exponential term:
6*16^x = 12216^x = 122/616^x = 61/3
Now, we can rewrite 61/3 as a power of 16:
16^x = 16^(61/3)x = 61/3
Therefore, the solution to the equation is x = 61/3.
To solve this equation, we need to first rewrite it in terms of powers of 2 and 4:
216^x - 32^4x - 1 + 7*4^2x - 1 = 120
Since 16 = 2^4 and 4 = 2^2, we can rewrite the equation as:
22^(4x) - 32^(4x) - 1 + 7(2^2)^(2x) - 1 = 120
22^(4x) - 32^(4x) - 1 + 72^(4x) - 1 = 120
22^(4x) - 32^(4x) + 72^(4x) - 2 = 120
62^(4x) - 2 = 120
6*16^x - 2 = 120
Next, we can isolate the exponential term:
6*16^x = 122
16^x = 122/6
16^x = 61/3
Now, we can rewrite 61/3 as a power of 16:
16^x = 16^(61/3)
x = 61/3
Therefore, the solution to the equation is x = 61/3.