Learn how to solve problems step by step online. Solve the exponential equation 125^(x-1)=25^(x+1). Wenden Sie die Formel an: x^b=pfgmin\left(x\right)^b, wobei b=x-1 und x=125. Simplify \left(5^{3}\right)^{\left(x-1\right)} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 3 and n equals x-1. Wenden Sie die Formel an: x^a=y^b\to x^a=pfgg\left(y,x\right)^b, wobei a=3\left(x-1\right), b=x+1, x=5, y=25, x^a=5^{3\left(x-1\right)}, x^a=y^b=5^{3\left(x-1\right)}=25^{\left(x+1\right)} und y^b=25^{\left(x+1\right)}. Simplify \left(5^{2}\right)^{\left(x+1\right)} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 2 and n equals x+1.

Solve the exponential equation 125^(x-1)=25^(x+1)