Need assistance in solving exponential equation: $\frac{27^x}{9^{2x-1}}=3^{x+4}$

Question

Find value of x: $$\frac{27^x}{9^{2x-1}}=3^{x+4}$$

My steps: $$\frac{(3^3)^x}{(3^2)^{2x-1}}=3^{x+4}$$ $$\frac{3x}{4x-2}=x+4$$

Please help me finish solving, and correct me if what I did so far has mistakes. Thanks very much.

Answer 1

Note that $\dfrac{(3^{3})^{x}}{(3^{2})^{2x-1}}=3^{2-x}=3^{x+4}$, then $2-x=x+4$

Answer 2

Your last step doesn't work, instead do: $$ 3^{3x - (4x - 2)} = 3^{x+4}. $$