Use the Properties of Logarithms to condense the logarithm below. Simplify, if possible. $$\frac{1}{2}\left(\log_5\left(r-4\right)-\log_5r\right)$$

$$\log_5\left(\sqrt[]{\frac{r-4}{r}}\right)$$

$$\log_5\left(\frac{\sqrt[]{r-4}}{r}\right)$$

$$\log_5\left(\sqrt[]{\frac{r-4}{2r}}\right)$$

$$\log_5\left(\frac{r-4}{\sqrt[]{r}}\right)$$

Expand: $$\log_5\left(\frac{\sqrt[3]{m}\cdot\sqrt[7]{n}}{k^2}\right)$$

$$\frac{1}{3}\log_5m+\frac{1}{7}\log_5n-2\log_5k$$

$$\frac{1}{3}\log_5m\cdot\frac{1}{7}\log_5n\div2\log_5k$$

$$\frac{3}{5}\log_5m+\frac{7}{5}\log_5n-\frac{2}{5}\log_5k$$

Use properties of logarithms to condense the logarithmic expression. $$\left(\log_aq-\log_ar\right)+2\log_ap$$

$$\log_a\left(\frac{qp^2}{r}\right)$$

$$\log_a\left(\frac{q}{p^2r}\right)$$

$$\log_a\left(\frac{2qp}{r}\right)$$

Use properties of logarithms to condense the logarithmic expression. $$\log_a\left(\frac{x^4\cdot\sqrt[3]{x+5}}{\left(x-2\right)^2}\right)$$

$$4\log_a\left(x\right)+\frac{1}{3}\log_a\left(x+5\right)-2\log_a\left(x-2\right)$$

$$\log_a\left(x^4\right)+\log_a\left(x+5\right)^{\frac{1}{3}}-\log_a\left(x-2\right)^2$$

$$\log_a\left(x^4\right)+\log_a\left(x+5\right)^{-3}-\log_a\left(x-2\right)^2$$

$$4\log_a\left(x\right)-3\log_a\left(x+5\right)-2\log_a\left(x-2\right)$$

Condense this expression to a single logarithm. $$\log_4\left(\frac{u^2}{w^2v^6}\right)$$

$$\log_4u^2-\log_4w^2+\log_4v^6$$

$$\log_4u^2-\log_4w^2-\log_4v^6$$

Use the Properties of Logarithms to expand the logarithm. Simplify if possible. $$\log_5\left(\sqrt[]{125xy^3}\right)$$

$$\frac{3}{2}+\frac{1}{2}\log_5x+\frac{3}{2}\log_5y$$

$$\frac{1}{2}\log_5125+\frac{1}{2}\log_5x+\frac{1}{2}\log_5y$$

$$\frac{1}{2}+\frac{1}{2}\log_5x+\frac{3}{2}\log_5y$$

Use the Properties of Logarithms to expand the logarithm. Simplify if possible. $$\log\left(\frac{2\left(x+y\right)^3}{z^2}\right)$$

$$\log2+3\log\left(x+y\right)-2\log z$$

$$3\log2-3\log\left(x+y\right)+2\log z$$

$$\log2-3\log\left(x+y\right)+2\log z$$

$$3\log2+3\log\left(x+y\right)-2\log z$$

Condense each expression to a single logarithm. $$\log_23-2\log_2x+\frac{1}{2}\log_2y-4\log_2z$$

$$\log_2\left(\frac{3\sqrt[]{y}}{x^2z^4}\right)$$

$$\log_2\left(\frac{3x^2}{z^4\sqrt[]{y}}\right)$$

$$\log_2\left(\frac{3z^4}{x^2\sqrt[]{y}}\right)$$

$$\log_2\left(\frac{x^2\sqrt[]{y}}{3z^4}\right)$$

Condense each expression to a single logarithm. $$\frac{1}{3}(\ln x+2\ln y)−(3\ln2+\ln z)$$

$$\ln\left(\frac{\sqrt[3]{xy^2}}{8z}\right)$$

$$\ln\left(\frac{\sqrt[3]{xy^2}}{8z^3}\right)$$

$$\ln\left(\frac{y^2\sqrt[3]{x}}{8z^3}\right)$$

$$\ln\left(\frac{y^2\sqrt[3]{x}}{8z}\right)$$

Use the Properties of Logarithms to expand the logarithm. $$\log_2\left(\frac{\sqrt[]{2x+y^2}}{8z^2}\right)$$

$$\frac{1}{2}\log_2\left(2x+y^2\right)-3-2\log_2z$$

$$2\log_2\left(2x+y^2\right)-3+2\log_2z$$

$$2\log_2\left(2x+y^2\right)-3-2\log_2z$$

$$\frac{1}{2}\log_2\left(2x+y^2\right)-3+2\log_2z$$

Logarithmic Properties

Quiz

•

Mathematics

•

11th Grade

•

Practice Problem

•

Medium

Josephine Quibido

Used 5+ times

FREE Resource

20 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

6

3

2

4

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MULTIPLE CHOICE QUESTION

45 sec • 1 pt

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3.

MULTIPLE CHOICE QUESTION

45 sec • 1 pt

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MULTIPLE CHOICE QUESTION

45 sec • 1 pt

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1

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-1

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MULTIPLE CHOICE QUESTION

45 sec • 1 pt

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MULTIPLE CHOICE QUESTION

45 sec • 1 pt

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MULTIPLE CHOICE QUESTION

45 sec • 1 pt

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