로그의 뜻과 성질

In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible.

${\log }_{7}3+{\log }_{7}x-{\log }_{7}y$

In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible.

${\log }_{5}2-{\log }_{5}x-{\log }_{5}y$

In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible.

$4{\log }_{2}x+6{\log }_{2}y$

In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible.

$6{\log }_{3}x+9{\log }_{3}y$

In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible.

${\log }_{3}({x}^{2}-1)-2{\log }_{3}(x-1)$

In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible.

$\log ({x}^{2}+2x+1)-2\log (x+1)$

In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible.

$4\log \,x-2\log y-3\log z$

In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible.

$3\ln \,x+4\ln \,y-2\ln \,z$

In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible.

$\frac{1}{3}\log \,x-3\log (x+1)$

In the following exercises, use the Properties of Logarithms to condense the logarithm. Simplify if possible.

$2\log (2x+3)+\frac{1}{2}\log (x+1)$

Use the Change-of-Base Formula

In the following exercises, use the Change-of-Base Formula, rounding to three decimal places, to approximate each logarithm.

${\log }_{3}42$

Use the Change-of-Base Formula

In the following exercises, use the Change-of-Base Formula, rounding to three decimal places, to approximate each logarithm.

${\log }_{5}46$

Use the Change-of-Base Formula

In the following exercises, use the Change-of-Base Formula, rounding to three decimal places, to approximate each logarithm.

${\log }_{12}87$

Use the Change-of-Base Formula

In the following exercises, use the Change-of-Base Formula, rounding to three decimal places, to approximate each logarithm.

${\log }_{15}93$

Use the Change-of-Base Formula

In the following exercises, use the Change-of-Base Formula, rounding to three decimal places, to approximate each logarithm.

${\log }_{\sqrt{2}}17$

Use the Change-of-Base Formula

In the following exercises, use the Change-of-Base Formula, rounding to three decimal places, to approximate each logarithm.

${\log }_{\sqrt{3}}21$

Write the Product Property in your own words. Does it apply to each of the following? ${\log }_{a}5x,$ ${\log }_{a}(5+x).$ Why or why not?

Write the Power Property in your own words. Does it apply to each of the following? ${\log }_{a}{x}^{p},$ ${({\log }_{a}x)}^{r}.$ Why or why not?

Use an example to show that $\log (a+b)\ne \log a+\log b.$

Explain how to find the value of ${\log }_{7}15$ using your calculator.