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# write each expression as a single logarithm in simplest form. state any restrictions on the variable.

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write each expression as a single logarithm in simplest form.  state any restrictions on the variable.

Guest Apr 14, 2017
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write each expression as a single logarithm in simplest form. state any restrictions on the variable.

$$log_3\frac{\sqrt{x}}{x}+log_3\sqrt[5]{x^2}+\frac{3}{2}log_3x$$

$$=log_3\frac{\sqrt{x}\cdot \sqrt[5]{x^2}\cdot \sqrt{x^3}}{x}$$

$$=log_3(x^{\frac{1}{2}+\frac{2}{5}+\frac{3}{2}-1})$$

$$=log_3(x^{1.4})$$

$$=1.4\times log_3(x)$$

!

asinus  Apr 15, 2017