Exercise
$\log_b\left(x\right)=\frac{3}{2}\log_b\left(16\right)-\frac{2}{3}\log_b\left(8\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Solve the logarithmic equation logb(x)=3/2logb(16)-2/3logb(8). Apply the formula: a\log_{b}\left(x\right)=\log_{b}\left(x^a\right). Using the power rule of logarithms: n\log_b(a)=\log_b(a^n). The difference of two logarithms of the same base b is equal to the logarithm of the quotient of the arguments, in other words: \log_b(M)-\log_b(N)=\log_b\left(\frac{M}{N}\right). Calculate the power \sqrt[3]{\left(8\right)^{2}}.
Solve the logarithmic equation logb(x)=3/2logb(16)-2/3logb(8)
Final answer to the exercise
$x=16$