True or False $$\ln\left(x+3\right)-\ln\left(2x\right)=\frac{\ln\left(x+3\right)}{\ln\left(2x\right)}$$

False, subtraction between two logarithms is division within a single logarithm in condensed form.

True, subtraction between two logarithms converts to division of those two logarithms in condensed form.

True, a logarithm is an exponent. When dividing like bases you subtract exponents, therefore dividing logarithms as in this example.

False, it is not possible to condense the expression.

1/3 log x + 1/3 log y + 1/3 log z

1/3 log x - 1/3 log y - 1/3 log z

log (x) + log (x) = log (25)

No solution (extraneous solutions)

Solve the equation: $$\log_4\left(2x^2+1\right)\ =\ \log_4\left(10x\ -\ 7\right)$$

undefined (extraneous solutions)

No solution, only extraneous solutions

Resource Library

Math

Logarithms

Logarithmic Equations

Solving Logarithmic Equations With Properties

Solving Logarithmic Equations with Properties

Authored by Barbara White

Mathematics

9th Grade - University

CCSS covered

Solving Logarithmic Equations with Properties

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30 questions

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MULTIPLE CHOICE QUESTION

30 sec • 1 pt

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Write as a single logarithm: log12 + 2logx

log (12 + 2x)

log (14x)

log (24x)

log (12x²)

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

The common logarithm has what base?

-e

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Logarithmic functions are the inverse of...

Linear Functions

Exponential Functions

Quadratic Functions

Polynomial Functions

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Rewrite log_pt = m in exponential form.

p^t = m

t^m = p

m^t = p

p^m = t

Use the change of base property to rewrite as a single logarithm:

$\frac{\log15}{\log3}$

$\log\ \frac{1}{5}$

$\log5$

$\log_{15}3$

$\log_315$

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

True or False:
log 12 - log 4 = log 8

True

False

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$-2\log3=\log\frac{1}{9}$
True or False:

True

False

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Choose the correctly condensed logarithm

$\frac{1}{2}\log_6a-\log_6b+\log_66$

$\log_6\left(\frac{6\sqrt{a}}{b}\right)\$

$\log_6\left(\frac{\sqrt{a}}{b}+1\right)\ \$

$\log_6\left(\frac{\sqrt{a}}{b}\right)\ \ +1$

$\log_6\left(\frac{\sqrt{a}}{b}\right)\ \ +6$

10.

FILL IN THE BLANKS QUESTION

30 sec • 1 pt

Use the properties of logarithms to find the exact value of each expression.

$\log_a1=$

(a)

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Solving Logarithmic Equations with Properties

Write as a single logarithm: log12 + 2logx

The common logarithm has what base?

Logarithmic functions are the inverse of...

Rewrite logpt = m in exponential form.

Use the change of base property to rewrite as a single logarithm: log⁡15log⁡3\frac{\log15}{\log3}log3log15​

True or False:log 12 - log 4 = log 8

−2log⁡3=log⁡19-2\log3=\log\frac{1}{9}−2log3=log91​ True or False:

Choose the correctly condensed logarithm 12log⁡6a−log⁡6b+log⁡66\frac{1}{2}\log_6a-\log_6b+\log_6621​log6​a−log6​b+log6​6

Use the properties of logarithms to find the exact value of each expression. log⁡a1=\log_a1=loga​1= (a)

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Discover more resources for Mathematics

Rewrite log_pt = m in exponential form.

Use the change of base property to rewrite as a single logarithm:

$\frac{\log15}{\log3}$

True or False:
log 12 - log 4 = log 8

$-2\log3=\log\frac{1}{9}$
True or False:

Choose the correctly condensed logarithm

$\frac{1}{2}\log_6a-\log_6b+\log_66$

Use the properties of logarithms to find the exact value of each expression.

$\log_a1=$

(a)