Question

5^2x+4×5^-x+1-125=0​

Answer 1

Take 5^x as y.

Now the question becomes a simple equation.

y + 20y - 125 = 0.

21y = 125.

Thus, y = 125/21.

Now resubstituting we get,

5^x = 125 /21.

Taking log on both sides,

xlog5 = log 125 - log 21

x = (log125/log5) - (log21/log 5)

x= 3- 1.89