2*3^x+1-3=15 3*5^x+3+2*5^x+1=77

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We can solve these equations by first simplifying the expressions on the left side of the equations.

1) 23^x + 1 - 3 = 15
23^x - 2 = 15
2*3^x = 17
3^x = 17 / 2
3^x = 8.5
x = log3(8.5)
x ≈ 1.305

2) 35^x + 3 + 25^x + 1 = 77
5^x(3 + 2) + 4 = 77
5^x(5) = 73
5^x = 73 / 5
x = log5(14.6)
x ≈ 1.123

Therefore, the solutions to the equations are x ≈ 1.305 and x ≈ 1.123.