Choose the correctly expanded natural logarithm: ln ⁡ ( 7 a b c ) \ln\left(\frac{7a}{bc}\right)\ ln ( b c 7 a )

ln ⁡ 7 + ln ⁡ a − ln ⁡ b − ln ⁡ c \ln7+\ln a-\ln b-\ln c ln 7 + ln a − ln b − ln c

ln ⁡ 7 + ln ⁡ a − ln ⁡ b + ln ⁡ c \ln7+\ln a-\ln b+\ln c ln 7 + ln a − ln b + ln c

ln ⁡ ( 7 a ) − ln ⁡ ( b c ) \ln(7a)-\ln(bc) ln ( 7 a ) − ln ( b c )

7 ln ⁡ a − b ln ⁡ c 7\ln a-b\ln c 7 ln a − b ln c

Choose the correctly condensed logarithm 1 2 log ⁡ 6 m − log ⁡ 6 n + log ⁡ 6 6 \frac{1}{2}\log_6m-\log_6n+\log_66 2 1 lo g 6 m − lo g 6 n + lo g 6 6

log ⁡ 6 ( m n ) + 1 \log_6\left(\frac{\sqrt{m}}{n}\right)\ \ +1 lo g 6 ( n m <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> ) + 1

log ⁡ 6 ( 6 m n ) \log_6\left(\frac{6\sqrt{m}}{n}\right)\ lo g 6 ( n 6 m <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> )

log ⁡ 6 ( m n + 1 ) \log_6\left(\frac{\sqrt{m}}{n}+1\right)\ \ lo g 6 ( n m <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> + 1 )

log ⁡ 6 ( m n ) + 6 \log_6\left(\frac{\sqrt{m}}{n}\right)\ \ +6 lo g 6 ( n m <path d="M95,702c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5, -10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8, -50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0, 35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5, -221c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467 s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422 s-65,47,-65,47z M834 80H400000v40H845z"> ) + 6

Solve for the exact value of x in the exponential equation. 2 4 x − 1 = 3 x + 1 2^{4x-1}=3^{x+1} 2 4 x − 1 = 3 x + 1 Then approximate your answer to the nearest hundreth.

x = log ⁡ ( 6 ) log ⁡ ( 16 3 ) , T h e r e f o r e x = 1.07 x=\frac{\log\left(6\right)}{\log\left(\frac{16}{3}\right)},\ \ Therefore\ x=1.07 x = lo g ( 3 1 6 ) lo g ( 6 ) , T h e r e f o r e x = 1 . 0 7

x = log ⁡ 3 − log ⁡ 2 4 log ⁡ 2 − log ⁡ 3 , T h e r e f o r e x = 0.24 x=\frac{\log3-\log2}{4\log2-\log3},\ \ Therefore\ x=0.24 x = 4 lo g 2 − lo g 3 lo g 3 − lo g 2 , T h e r e f o r e x = 0 . 2 4

x = log ⁡ 6 4 ( log ⁡ 2 − log ⁡ 3 ) , T h e r e f o r e x = − 1.10 x=\frac{\log6}{4\left(\log2-\log3\right)},\ \ Therefore\ x=-1.10 x = 4 ( lo g 2 − lo g 3 ) lo g 6 , T h e r e f o r e x = − 1 . 1 0

x = 4 log ⁡ 3 ( log ⁡ 2 − log ⁡ 3 ) , T h e r e f o r e x = − 10.84 x=\frac{4\log3}{\left(\log2-\log3\right)},\ \ Therefore\ x=-10.84 x = ( lo g 2 − lo g 3 ) 4 lo g 3 , T h e r e f o r e x = − 1 0 . 8 4

Determine the rate that represents the better deal.

3.25% interest rate compounded annually

3% interest rate compounded continuously

What percent of a parent isotope remains after one half life?

50% of the parent isotope remains

1/2 of the parent isotope remains.

One out of two of the parent isotopes remain.

.5% of the parent isotope remains

#4 Solving Expo & Log Equations

Quiz

•

Mathematics

•

9th - 12th Grade

•

Practice Problem

•

Medium

•

CCSS

HSA.SSE.A.2, HSF.LE.A.4, HSA.SSE.B.3

+2

Standards-aligned

Shayla Bushhousen

Used 24+ times

FREE Resource

27 questions

Show all answers

1.

FILL IN THE BLANK QUESTION

30 sec • 1 pt

Find the exact value of the logarithm without using a calculator.

$\log_{\sqrt{5}}25$

2.

FILL IN THE BLANK QUESTION

30 sec • 1 pt

Solve the logarithmic equation.

$\log_7343=2x+1$

x = __________

3.

FILL IN THE BLANK QUESTION

30 sec • 1 pt

Solve the logarithmic equation.

$\log_6\sqrt{x-2}=2$

x = __________

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

Choose the correctly expanded natural logarithm:

$\ln\left(\frac{7a}{bc}\right)\$

$\ln7+\ln a-\ln b-\ln c$

$\ln7+\ln a-\ln b+\ln c$

$\ln(7a)-\ln(bc)$

$7\ln a-b\ln c$

5.

MULTIPLE CHOICE QUESTION

1 min • 1 pt

Choose the correctly condensed common logarithm

$\log q+\log r+3\log s$

$\log\left(qrs^3\right)$

$\log\left(qrs\right)^3\ \ \ \$

$\log\left(3qrs\right)\ \ \ \ \$

$3\log\left(qrs\right)$

Choose the correctly condensed logarithm

$\frac{1}{2}\log_6m-\log_6n+\log_66$

$\log_6\left(\frac{6\sqrt{m}}{n}\right)\$

$\log_6\left(\frac{\sqrt{m}}{n}+1\right)\ \$

$\log_6\left(\frac{\sqrt{m}}{n}\right)\ \ +1$

$\log_6\left(\frac{\sqrt{m}}{n}\right)\ \ +6$

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

$e^{\ln4}=$

8.

FILL IN THE BLANK QUESTION

15 mins • 1 pt

Solve for x in the logarithmic equation.

$\log_3(4x-3)=2$

9.

FILL IN THE BLANK QUESTION

15 mins • 1 pt

Solve for x in the logarithmic equation.

$\log_2(x+6)+\log_2\left(x-1\right)=3$

10.

FILL IN THE BLANK QUESTION

15 mins • 1 pt

Solve for x in the logarithmic equation.

$\log_5(3x-1)=\log_5(2x+5)$

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#4 Solving Expo & Log Equations

27 questions

Find the exact value of the logarithm without using a calculator. log⁡525\log_{\sqrt{5}}25log5​​25

Solve the logarithmic equation. log⁡7343=2x+1\log_7343=2x+1log7​343=2x+1 x = __________

Solve the logarithmic equation. log⁡6x−2=2\log_6\sqrt{x-2}=2log6​x−2​=2 x = __________

Choose the correctly expanded natural logarithm: ln⁡(7abc) \ln\left(\frac{7a}{bc}\right)\ ln(bc7a​)

Choose the correctly condensed common logarithm log⁡q+log⁡r+3log⁡s\log q+\log r+3\log slogq+logr+3logs

Choose the correctly condensed logarithm 12log⁡6m−log⁡6n+log⁡66\frac{1}{2}\log_6m-\log_6n+\log_6621​log6​m−log6​n+log6​6

Use the properties of logarithms to find the exact value of each expression. eln⁡4=e^{\ln4}=eln4=

Solve for x in the logarithmic equation. log⁡3(4x−3)=2\log_3(4x-3)=2log3​(4x−3)=2

Solve for x in the logarithmic equation. log⁡2(x+6)+log⁡2(x−1)=3\log_2(x+6)+\log_2\left(x-1\right)=3log2​(x+6)+log2​(x−1)=3

Solve for x in the logarithmic equation. log⁡5(3x−1)=log⁡5(2x+5)\log_5(3x-1)=\log_5(2x+5)log5​(3x−1)=log5​(2x+5)

Access all questions and much more by creating a free account

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Find the exact value of the logarithm without using a calculator.

$\log_{\sqrt{5}}25$

Solve the logarithmic equation.

$\log_7343=2x+1$

x = __________

Solve the logarithmic equation.

$\log_6\sqrt{x-2}=2$

x = __________

Choose the correctly expanded natural logarithm:

$\ln\left(\frac{7a}{bc}\right)\$

Choose the correctly condensed common logarithm

$\log q+\log r+3\log s$

Choose the correctly condensed logarithm

$\frac{1}{2}\log_6m-\log_6n+\log_66$

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

$e^{\ln4}=$

Solve for x in the logarithmic equation.

$\log_3(4x-3)=2$

Solve for x in the logarithmic equation.

$\log_2(x+6)+\log_2\left(x-1\right)=3$

Solve for x in the logarithmic equation.

$\log_5(3x-1)=\log_5(2x+5)$