Exercise
$3\cdot2^{3y}=7\cdot3^{3x-2}$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the exponential equation 3*2^(3y)=7*3^(3x-2). Apply natural logarithm to both sides of the equation. Applying the product rule for logarithms: \log_b\left(MN\right)=\log_b\left(M\right)+\log_b\left(N\right). Using the power rule of logarithms: \log_a(x^n)=n\cdot\log_a(x). Using the power rule of logarithms: n\log_b(a)=\log_b(a^n).
Solve the exponential equation 3*2^(3y)=7*3^(3x-2)
Final answer to the exercise
$y=\frac{\ln\left(\frac{7\cdot 3^{\left(3x-2\right)}}{3}\right)}{\ln\left(8\right)}$