Math
posted by Moku on .
Solve the following exponential equation
5^2x=7^5x+7

5 ^ 2 = 25
7 ^ 5 = 16,807
5 ^ 2  x = 7 ^ 5 x + 7
25  x = 16,807 x + 7 Add x to both sides
25  x + x = 16,807 x + 7 + x
25 = 16,808 x + 7 Subtract 7 to both sides
25  7 = 16,808 x + 7  7
18 = 16,808 x Divide both sides by 16,808
18 / 16,808 = 16,808 x / 16,808
18 / 16,808 = x
2 * 9 / ( 2 * 8,404 ) = x
9 / 8,404 = x
x = 9 / 8,404 
If you mean,
5^(2x) = 7^(5x + 7)
Then, we take the ln of both sides
(2x)*ln(5) = (5x + 7)*ln(7)
1.609*(2x) = 1.946*(5x+7)
Solving for x,
x = 0.9174
Hope this helps :3