Learn how to solve problems step by step online. Solve the exponential equation 3^(4x)=27^(x-3). Wenden Sie die Formel an: x^a=y^b\to x^a=pfgg\left(y,x\right)^b, wobei a=4x, b=x-3, x=3, y=27, x^a=3^{4x}, x^a=y^b=3^{4x}=27^{\left(x-3\right)} und y^b=27^{\left(x-3\right)}. Simplify \left(3^{3}\right)^{\left(x-3\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-3. Wenden Sie die Formel an: a^b=a^c\to b=c, wobei a=3, b=4x und c=3\left(x-3\right). Wenden Sie die Formel an: x\left(a+b\right)=xa+xb, wobei a=x, b=-3, x=3 und a+b=x-3.

Solve the exponential equation 3^(4x)=27^(x-3)