Exercise
$\frac{3}{2}\ln\left(4x^{10}\right)-\frac{1}{5}\ln\left(2y^{30}\right)$
Step-by-step Solution
Learn how to solve problems step by step online. Condense the logarithmic expression 3/2ln(4x^10)-1/5ln(2y^30). Using the power rule of logarithms: n\log_b(a)=\log_b(a^n), where n equals \frac{3}{2}. The power of a product is equal to the product of it's factors raised to the same power. Simplify \sqrt{\left(x^{10}\right)^{3}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 10 and n equals \frac{3}{2}. Using the power rule of logarithms: n\log_b(a)=\log_b(a^n).
Condense the logarithmic expression 3/2ln(4x^10)-1/5ln(2y^30)
Final answer to the exercise
$\ln\left(\frac{8x^{15}}{\sqrt[5]{2}y^{6}}\right)$