Final answer to the problem
$x=\frac{\ln\left(\frac{2}{3}\right)}{\ln\left(2\right)-\ln\left(9\right)}$
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Step-by-step Solution
Learn how to solve exponential equations problems step by step online. Solve the exponential equation 2^(x-1)=3^(2x-1). Apply natural logarithm to both sides of the equation. Solve the product \ln\left(2\right)\left(x-1\right). Solve the product \ln\left(3\right)\left(2x-1\right). Using the power rule of logarithms: n\log_b(a)=\log_b(a^n).
Final answer to the problem
$x=\frac{\ln\left(\frac{2}{3}\right)}{\ln\left(2\right)-\ln\left(9\right)}$
Exact Numeric Answer
$x=0.2695773$
