Ms. Jones isn't sure if she solved this logarithmic equation correctly. Check her work to determine if she made any mistakes. If she did make a mistake, determine what it was.

She did not distribute the 4 when combining the logs.

She did not convert to exponential form correctly.

She should have subtracted 2 from both sides instead of adding 2.

Mrs. Cruise isn't sure if she solved this logarithmic equation correctly. Check her work to determine if she made any mistakes. If she did make a mistake, determine what it was.

She used the incorrect base when converting to exponential form.

She did not convert to exponential form correctly.

She should have divided the arguments.

Solving Logarithmic Functions

Authored by Theresa Jones

Mathematics

10th - 12th Grade

CCSS covered

Used 62+ times

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12 questions

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FILL IN THE BLANKS QUESTION

1 min • 1 pt

$\log_3\left(x\right)=4$

Solve for x. Enter only numbers in your answer.

(a)

Tags

CCSS.HSF.BF.B.5

FILL IN THE BLANKS QUESTION

1 min • 1 pt

$\log_5\left(x-7\right)=2$
Solve for x. Enter only numbers in your answer.

(a)

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.REI.A.1

CCSS.HSF.LE.A.4

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\log_4\left(3x+2\right)=3$
Solve for x.

20.67

26.33

27.67

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.REI.A.1

CCSS.HSA.CED.A.1

FILL IN THE BLANKS QUESTION

1 min • 1 pt

$\log_6\left(x+5\right)+\log_6\left(4\right)=2$
Solve for x. Enter only numbers in your answer.

(a)

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.REI.A.1

CCSS.HSA.CED.A.1

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\log_5\left(x^5\right)-\log_5\left(x^3\right)=2$

Which of the follow best describes why $x=-5$ is an extraneous solution to the equation above?

Hint: Try plugging in -5 and simplifying!

-5 does not match the base of the logarithms.

-5 is less than the output of the equation.

Plugging in -5 for x results in a negative argument.

Plugging in -5 for x results in a positive argument.

Tags

CCSS.HSA.REI.A.2

CCSS.HSF.IF.B.5

FILL IN THE BLANKS QUESTION

1 min • 1 pt

$\log_2\left(x^2+2x\right)-\log_2\left(x\right)=3$
Solve for x. Enter only numbers in your answer.

(a)

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

FILL IN THE BLANKS QUESTION

1 min • 1 pt

$-6\log_3\left(x-3\right)=-24$
Solve for x. Enter only numbers in your answer.

(a)

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.REI.A.1

CCSS.HSF.LE.A.4

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\ln\left(x^3+3x\right)-\ln\left(x\right)=4$
Solve for x.

$x=99.98$ and $x=-99.98$ (extraneous)

$x=99.98$ and $x=-99.98$ , no extraneous solutions

$x=7.18$ and $x=-7.18$ (extraneous)

$x=7.18$ and $x=-7.18$ , no extraneous solutions

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.REI.A.1

CCSS.HSF.LE.A.4

CCSS.HSA.REI.A.2

FILL IN THE BLANKS QUESTION

1 min • 1 pt

$2\log_3\left(x+4\right)=2$
Solve for x. Enter only numbers in your answer.

(a)

Tags

CCSS.HSF.BF.B.5

CCSS.HSA.REI.A.1

CCSS.HSF.LE.A.4

10.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

$\log_8\left(2\right)+\log_8\left(4x^2\right)=1$
Solve for x.

$x=1$ and $x=-1$ , no extraneous solutions

$x=1$ and $x=-1$ (extraneous)

$x=4$ and $x=-4$ , no extraneous solutions

$x=4$ and $x=-4$ (extraneous)

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

CCSS.HSA.REI.A.2

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Solving Logarithmic Functions

log⁡3(x)=4\log_3\left(x\right)=4log3​(x)=4 Solve for x. Enter only numbers in your answer. (a)

log⁡5(x−7)=2\log_5\left(x-7\right)=2log5​(x−7)=2 Solve for x. Enter only numbers in your answer. (a)

log⁡4(3x+2)=3\log_4\left(3x+2\right)=3log4​(3x+2)=3 Solve for x.

log⁡6(x+5)+log⁡6(4)=2\log_6\left(x+5\right)+\log_6\left(4\right)=2log6​(x+5)+log6​(4)=2 Solve for x. Enter only numbers in your answer. (a)

log⁡5(x5)−log⁡5(x3)=2\log_5\left(x^5\right)-\log_5\left(x^3\right)=2log5​(x5)−log5​(x3)=2 Which of the follow best describes why x=−5x=-5x=−5 is an extraneous solution to the equation above?Hint: Try plugging in -5 and simplifying!

log⁡2(x2+2x)−log⁡2(x)=3\log_2\left(x^2+2x\right)-\log_2\left(x\right)=3log2​(x2+2x)−log2​(x)=3 Solve for x. Enter only numbers in your answer. (a)

−6log⁡3(x−3)=−24-6\log_3\left(x-3\right)=-24−6log3​(x−3)=−24 Solve for x. Enter only numbers in your answer. (a)

ln⁡(x3+3x)−ln⁡(x)=4\ln\left(x^3+3x\right)-\ln\left(x\right)=4ln(x3+3x)−ln(x)=4 Solve for x.

2log⁡3(x+4)=22\log_3\left(x+4\right)=22log3​(x+4)=2 Solve for x. Enter only numbers in your answer. (a)

log⁡8(2)+log⁡8(4x2)=1\log_8\left(2\right)+\log_8\left(4x^2\right)=1log8​(2)+log8​(4x2)=1 Solve for x.

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$\log_3\left(x\right)=4$

Solve for x. Enter only numbers in your answer.

(a)

$\log_5\left(x-7\right)=2$
Solve for x. Enter only numbers in your answer.

(a)

$\log_4\left(3x+2\right)=3$
Solve for x.

$\log_6\left(x+5\right)+\log_6\left(4\right)=2$
Solve for x. Enter only numbers in your answer.

(a)

$\log_5\left(x^5\right)-\log_5\left(x^3\right)=2$

Which of the follow best describes why $x=-5$ is an extraneous solution to the equation above?

Hint: Try plugging in -5 and simplifying!

$\log_2\left(x^2+2x\right)-\log_2\left(x\right)=3$
Solve for x. Enter only numbers in your answer.

(a)

$-6\log_3\left(x-3\right)=-24$
Solve for x. Enter only numbers in your answer.

(a)

$\ln\left(x^3+3x\right)-\ln\left(x\right)=4$
Solve for x.

$2\log_3\left(x+4\right)=2$
Solve for x. Enter only numbers in your answer.

(a)

$\log_8\left(2\right)+\log_8\left(4x^2\right)=1$
Solve for x.