formula used to solve this equation: 5power of x+1 times 25power of x equals 5 power of 2x-3

Question

I need the formula used to sove for x in the equation.  5 to the power of x+1 times 25 to the power of x equals 5 to the power of 2x-3?

Answer 1

(5^(x+1)(25^x)=5^(2x-3). 25=5^2, so 25^x=5^(2x). Now everything is in terms of powers of 5.

We can combine the multiplication on the left: 5^(x+1+2x)=5^(2x-3). The power of 5 on the left matches the power of 5 on the right so 3x+1=2x-3 from which x=-4. Check by substituting for x in the original equation: 5^-3*25^-4=5^-3*(5*5)^-4=5^-3*5^-4*5^-4=5^(-3-4-4)=5^-11. On the right: 5^(-8-3)=5^-11. Checks out OK!