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The power of a quotient is equal to the quotient of the power of the numerator and denominator: $\displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}$
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$\ln\left(\frac{\sqrt{\left(x-8\right)^{26}}}{\sqrt{\left(3x-7\right)^{38}}}\right)$
Learn how to solve condensing logarithms problems step by step online. Condense the logarithmic expression ln((((x-8)^26)/((3x-7)^38))^1/2). The power of a quotient is equal to the quotient of the power of the numerator and denominator: \displaystyle\left(\frac{a}{b}\right)^n=\frac{a^n}{b^n}. Simplify \sqrt{\left(x-8\right)^{26}} using the power of a power property: \left(a^m\right)^n=a^{m\cdot n}. In the expression, m equals 26 and n equals \frac{1}{2}. Multiply 26 times \frac{1}{2}. Multiply 26 times \frac{1}{2}.