+129899 I think this might be
7^a -7^(a-5)=117642√7
We can write
7^a - 7^a / 7^5 = (2 * 3 * 2801) * 7 * 7^(1/2)
7^a - 7^a / 7^5 = (2 * 3 * 2801) * 7^(3/2) multiply through by 7^5
7^(a + 5) - 7^a = (2 * 3 * 2801) * 7^(13/2) factor
7^a ( 7^5 - 1) = (2 * 3 * 2801) * 7^(13/2)
7^a ( 16806) = ( 16806) * 7^(13/2) divide out 16806
7^a = 7^(13/2)
a ⇒ 13/2
Solve for a:
7^a - 7^(a - 5) = 117642 sqrt(7)
Simplify and substitute x = -7^(a - 5).
7^a - 7^(a - 5) = -16806 (-7^(a - 5))
= -16806 x:
-16806 x = 117642 sqrt(7)
Divide both sides by -16806:
x = -7 sqrt(7)
Substitute back for x = -7^(a - 5):
-7^(a - 5) = -7 sqrt(7)
Multiply both sides by -1:
7^(a - 5) = 7 sqrt(7)
Take the logarithm base 7 of both sides:
a - 5 = (log(7 sqrt(7)))/(log(7))
Add 5 to both sides:
a = 5 + (log(7 sqrt(7)))/(log(7))
Log here is the natural "ln".
