Impara online a risolvere i problemi di passo dopo passo. Solve the exponential equation 27^(x-1)=9^(2x-3). Applicare la formula: x^b=pfgmin\left(x\right)^b, dove b=x-1 e x=27. Simplify \left(3^{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. Applicare la formula: x^a=y^b\to x^a=pfgg\left(y,x\right)^b, dove a=3\left(x-1\right), b=2x-3, x=3, y=9, x^a=3^{3\left(x-1\right)}, x^a=y^b=3^{3\left(x-1\right)}=9^{\left(2x-3\right)} e y^b=9^{\left(2x-3\right)}. Simplify \left(3^{2}\right)^{\left(2x-3\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 2x-3.

Solve the exponential equation 27^(x-1)=9^(2x-3)