Impara online a risolvere i problemi di divisione di numeri passo dopo passo. Solve the exponential equation 3^(x-2)=9^(x+4). Applicare la formula: x^a=y^b\to x^a=pfgg\left(y,x\right)^b, dove a=x-2, b=x+4, x=3, y=9, x^a=3^{\left(x-2\right)}, x^a=y^b=3^{\left(x-2\right)}=9^{\left(x+4\right)} e y^b=9^{\left(x+4\right)}. Simplify \left(3^{2}\right)^{\left(x+4\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+4. Applicare la formula: a^b=a^c\to b=c, dove a=3, b=x-2 e c=2\left(x+4\right). Applicare la formula: x\left(a+b\right)=xa+xb, dove a=x, b=4, x=2 e a+b=x+4.

Solve the exponential equation 3^(x-2)=9^(x+4)