Simplify the expression. ln ⁡ ( x − 6 ) − ln ⁡ 4 + ln ⁡ 7 \ln\left(x-6\right)-\ln4+\ln7 ln ( x − 6 ) − ln 4 + ln 7

ln ⁡ ( 7 x − 42 4 ) \ln\left(\frac{7x-42}{4}\right) ln ( 4 7 x − 4 2 )

ln ⁡ ( 42 x − 7 4 ) \ln\left(\frac{42x-7}{4}\right) ln ( 4 4 2 x − 7 )

ln ⁡ ( 4 x − 7 42 ) \ln\left(\frac{4x-7}{42}\right) ln ( 4 2 4 x − 7 )

ln ⁡ ( 7 x − 4 42 ) \ln\left(\frac{7x-4}{42}\right) ln ( 4 2 7 x − 4 )

ln ⁡ ( 4 x − 42 7 ) \ln\left(\frac{4x-42}{7}\right) ln ( 7 4 x − 4 2 )

Simplify the expression. ln ⁡ ( x − 8 ) + ln ⁡ 2 − ln ⁡ 4 \ln\left(x-8\right)+\ln2-\ln4 ln ( x − 8 ) + ln 2 − ln 4

ln ⁡ ( x − 8 2 ) \ln\left(\frac{x-8}{2}\right) ln ( 2 x − 8 )

ln ⁡ ( 8 − x 2 ) \ln\left(\frac{8-x}{2}\right) ln ( 2 8 − x )

ln ⁡ ( 2 − x 8 ) \ln\left(\frac{2-x}{8}\right) ln ( 8 2 − x )

ln ⁡ ( x − 2 8 ) \ln\left(\frac{x-2}{8}\right) ln ( 8 x − 2 )

ln ⁡ ( 8 x − 2 x ) \ln\left(\frac{8x-2}{x}\right) ln ( x 8 x − 2 )

Solve for x . x. x . ( e x e 11 ) x = 1 e 30 \left(e^xe^{11}\right)^x=\frac{1}{e^{30}} ( e x e 1 1 ) x = e 3 0 1

x = − 6 , x = − 5 x=-6,\ x=-5 x = − 6 , x = − 5

x = 5 , x = 6 x=5,\ x=6 x = 5 , x = 6

x = 4 , x = 7 x=4,\ x=7 x = 4 , x = 7

x = − 4 , x = − 7 x=-4,\ x=-7 x = − 4 , x = − 7

Solve for x . x. x . 6 ( 3 x − 1 ) = 9 ( x − 4 ) 6^{\left(3x-1\right)}=9^{\left(x-4\right)} 6 ( 3 x − 1 ) = 9 ( x − 4 )

x = ln ⁡ 6 − 4 ln ⁡ 9 3 ln ⁡ 6 − ln ⁡ 9 x=\frac{\ln6-4\ln9}{3\ln6-\ln9} x = 3 ln 6 − ln 9 ln 6 − 4 ln 9

x = 3 ln ⁡ 6 − ln ⁡ 9 ln ⁡ 6 − 4 ln ⁡ 9 x=\frac{3\ln6-\ln9}{\ln6-4\ln9} x = ln 6 − 4 ln 9 3 ln 6 − ln 9

x = 4 ln ⁡ 9 − ln ⁡ 6 ln ⁡ 9 − 3 ln ⁡ 6 x=\frac{4\ln9-\ln6}{\ln9-3\ln6} x = ln 9 − 3 ln 6 4 ln 9 − ln 6

x = ln ⁡ 9 − 3 ln ⁡ 6 4 ln ⁡ 9 − ln ⁡ 6 x=\frac{\ln9-3\ln6}{4\ln9-\ln6} x = 4 ln 9 − ln 6 ln 9 − 3 ln 6

Solve for x . x. x . 8 ( 5 x − 1 ) = 1 1 ( x + 6 ) 8^{\left(5x-1\right)}=11^{\left(x+6\right)} 8 ( 5 x − 1 ) = 1 1 ( x + 6 )

x = ln ⁡ 8 + 6 ln ⁡ 11 5 ln ⁡ 8 − ln ⁡ 11 x=\frac{\ln8+6\ln11}{5\ln8-\ln11} x = 5 ln 8 − ln 1 1 ln 8 + 6 ln 1 1

x = ln ⁡ 8 − 6 ln ⁡ 11 5 ln ⁡ 8 + ln ⁡ 11 x=\frac{\ln8-6\ln11}{5\ln8+\ln11} x = 5 ln 8 + ln 1 1 ln 8 − 6 ln 1 1

x = ln ⁡ 11 − 5 ln ⁡ 8 6 ln ⁡ 11 + ln ⁡ 8 x=\frac{\ln11-5\ln8}{6\ln11+\ln8} x = 6 ln 1 1 + ln 8 ln 1 1 − 5 ln 8

x = 5 ln ⁡ 11 + ln ⁡ 8 ln ⁡ 11 − 6 ln ⁡ 8 x=\frac{5\ln11+\ln8}{\ln11-6\ln8} x = ln 1 1 − 6 ln 8 5 ln 1 1 + ln 8

Solve for x . x. x . log ⁡ 2 ( 1 8 ) = x \log_2\left(\frac{1}{8}\right)=x lo g 2 ( 8 1 ) = x

x = − 1 3 x=-\frac{1}{3} x = − 3 1

Solve for x . x. x . log ⁡ 49 ( 1 7 ) = x \log_{49}\left(\frac{1}{7}\right)=x lo g 4 9 ( 7 1 ) = x

x = − 1 2 x=-\frac{1}{2} x = − 2 1

Logs and Exponents Review

Authored by Mr. Kent

Mathematics

11th Grade - University

CCSS covered

Used 14+ times

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15 questions

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MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Simplify the expression.
$\ln\left(x-6\right)-\ln4+\ln7$

$\ln\left(\frac{7x-42}{4}\right)$

$\ln\left(\frac{42x-7}{4}\right)$

$\ln\left(\frac{4x-7}{42}\right)$

$\ln\left(\frac{7x-4}{42}\right)$

$\ln\left(\frac{4x-42}{7}\right)$

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Simplify the expression.
$\ln\left(x-8\right)+\ln2-\ln4$

$\ln\left(\frac{x-8}{2}\right)$

$\ln\left(\frac{8-x}{2}\right)$

$\ln\left(\frac{2-x}{8}\right)$

$\ln\left(\frac{x-2}{8}\right)$

$\ln\left(\frac{8x-2}{x}\right)$

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Write in expanded form.
$\log\left(\frac{\left(x-8\right)^3}{m}\right)$

$3\log\left(x-8\right)-\log m$

$3\log\left(x-8\right)+\log m$

$\log m-3\log\left(x-8\right)$

$\log\left(x-8\right)-3\log m$

$3\log\left(x+8\right)+\log m$

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Write in expanded form.
$\log\left(\frac{\left(3x+7\right)^4}{n}\right)$

$4\log\left(3x+7\right)-\log n$

$4\log\left(3x+7\right)+\log n$

$\log n-4\log\left(3x+7\right)$

$\log\left(3x+7\right)-3\log n$

$\frac{n-7}{3}$

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve for $x.$
$\log_3\left(x^2-19\right)=4$

$x=-10,\ x=10$

$x=10$

$x=-5,\ x=5$

$x=5$

$x=-25,\ x=25$

Solve for $x.$
$\log_4\left(x^3-61\right)=3$

$x=-10,\ x=10$

$x=10$

$x=-5,\ x=5$

$x=5$

$x=4$

Solve for $x.$
$\left(e^xe^{11}\right)^x=\frac{1}{e^{30}}$

$x=-6,\ x=-5$

$x=5,\ x=6$

$x=4,\ x=7$

$x=-4,\ x=-7$

DNE (Does not exist)

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve for $x.$
$\left(\frac{e^{2x}}{e^{14}}\right)^x=\frac{1}{e^{24}}$

$x=3,\ x=4$

$x=3$

$x=4$

$x=-3,\ x=-4$

DNE (Does not exist)

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve for $x.$
$\log_8\left(x-5\right)+\log_8\left(x+5\right)=\log_824$

$x=7$

$x=2$

$x=-7$

$x=10$

DNE (Does not exist)

10.

MULTIPLE CHOICE QUESTION

5 mins • 1 pt

Solve for $x.$
$\log_{11}\left(x-6\right)+\log_{11}\left(x+6\right)=\log_{11}28$

$x=7$

$x=8$

$x=3$

$x=10$

DNE (Does not exist)

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Logs and Exponents Review

Simplify the expression. ln⁡(x−6)−ln⁡4+ln⁡7\ln\left(x-6\right)-\ln4+\ln7ln(x−6)−ln4+ln7

Simplify the expression. ln⁡(x−8)+ln⁡2−ln⁡4\ln\left(x-8\right)+\ln2-\ln4ln(x−8)+ln2−ln4

Write in expanded form. log⁡((x−8)3m)\log\left(\frac{\left(x-8\right)^3}{m}\right)log(m(x−8)3​)

Write in expanded form. log⁡((3x+7)4n)\log\left(\frac{\left(3x+7\right)^4}{n}\right)log(n(3x+7)4​)

Solve for x.x.x. log⁡3(x2−19)=4\log_3\left(x^2-19\right)=4log3​(x2−19)=4

Solve for x.x.x. log⁡4(x3−61)=3\log_4\left(x^3-61\right)=3log4​(x3−61)=3

Solve for x.x.x. (exe11)x=1e30\left(e^xe^{11}\right)^x=\frac{1}{e^{30}}(exe11)x=e301​

Solve for x.x.x. (e2xe14)x=1e24\left(\frac{e^{2x}}{e^{14}}\right)^x=\frac{1}{e^{24}}(e14e2x​)x=e241​

Solve for x.x.x. log⁡8(x−5)+log⁡8(x+5)=log⁡824\log_8\left(x-5\right)+\log_8\left(x+5\right)=\log_824log8​(x−5)+log8​(x+5)=log8​24

Solve for x.x.x. log⁡11(x−6)+log⁡11(x+6)=log⁡1128\log_{11}\left(x-6\right)+\log_{11}\left(x+6\right)=\log_{11}28log11​(x−6)+log11​(x+6)=log11​28

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Discover more resources for Mathematics

Simplify the expression.
$\ln\left(x-6\right)-\ln4+\ln7$

Simplify the expression.
$\ln\left(x-8\right)+\ln2-\ln4$

Write in expanded form.
$\log\left(\frac{\left(x-8\right)^3}{m}\right)$

Write in expanded form.
$\log\left(\frac{\left(3x+7\right)^4}{n}\right)$

Solve for $x.$
$\log_3\left(x^2-19\right)=4$

Solve for $x.$
$\log_4\left(x^3-61\right)=3$

Solve for $x.$
$\left(e^xe^{11}\right)^x=\frac{1}{e^{30}}$

Solve for $x.$
$\left(\frac{e^{2x}}{e^{14}}\right)^x=\frac{1}{e^{24}}$

Solve for $x.$
$\log_8\left(x-5\right)+\log_8\left(x+5\right)=\log_824$

Solve for $x.$
$\log_{11}\left(x-6\right)+\log_{11}\left(x+6\right)=\log_{11}28$