Impara online a risolvere i problemi di passo dopo passo. Solve the exponential equation 2^8^(x-2)=4^4^(x-1). Applicare la formula: x^a=y^b\to x^a=pfgg\left(y,x\right)^b, dove a=8^{\left(x-2\right)}, b=4^{\left(x-1\right)}, x=2, y=4, x^a=2^{\left(8^{\left(x-2\right)}\right)}, x^a=y^b=2^{\left(8^{\left(x-2\right)}\right)}=4^{\left(4^{\left(x-1\right)}\right)} e y^b=4^{\left(4^{\left(x-1\right)}\right)}. Simplify \left(2^{2}\right)^{\left(4^{\left(x-1\right)}\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 4^{\left(x-1\right)}. Applicare la formula: a^b=a^c\to b=c, dove a=2, b=8^{\left(x-2\right)} e c=2\cdot 4^{\left(x-1\right)}. Applicare la formula: a^{\left(b+c\right)}=a^ba^c.

Solve the exponential equation 2^8^(x-2)=4^4^(x-1)