Final answer to the problem
$\ln\left(\frac{1024x^{15}}{\sqrt[5]{\left(2\right)^{2}}y^{12}}\right)$
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Step-by-step Solution
Learn how to solve condensing logarithms problems step by step online. Condense the logarithmic expression 5/2ln(16x^6)-2/5ln(2y^30). Using the power rule of logarithms: n\log_b(a)=\log_b(a^n), where n equals \frac{5}{2}. The power of a product is equal to the product of it's factors raised to the same power. Simplify \sqrt{\left(x^6\right)^{5}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 6 and n equals \frac{5}{2}. Using the power rule of logarithms: n\log_b(a)=\log_b(a^n).
Final answer to the problem
$\ln\left(\frac{1024x^{15}}{\sqrt[5]{\left(2\right)^{2}}y^{12}}\right)$
