3^5x-2=27 3 в степени 5x-2 равно 27

To solve the equation $3^{5x-2}=27$, we need to express both sides of the equation with the same base. 1. Transform the Equation First, recognize that 27 is a power of 3: $27=3^3$Now, substitute this back into the original equation: $3^{5x-2}=3^3$2. Equate the Exponents Since the bases are identical (both are 3), their exponents must be equal for the equation to hold true: $5x-2=3$3. Solve for x Now, perform basic algebraic operations to isolate $x$:

• Add 2 to both sides:
  $5x=3+2$ $5x=5$ Divide by 5:
  $x=\frac{5}{5}$ $x=1$

Answer: $x=1$ Verification: Substitute $x=1$ back into the original equation: $3^{5\left(1\right)-2}=3^{5-2}=3^3=27$. The solution is correct. Would you like me to solve another exponential equation using this method?