Natural Base and Natural Logarithms

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Write the equation in logarithmic form.
 $e^{\left(x-9\right)}=74$  

•  $\ln\left(x-9\right)=74$  

•  $x-9=\ln74$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Write the equation in exponential form. 
 $\ln53=x$   

•  $e^{53}=x$  

•  $e^x=53$  

Tags

CCSS.HSF.BF.B.5

Write the equation in exponential form. 
 $\ln87=x+4$  

•  $e^{\left(x+4\right)}=87$  

•  $e^{87}=x+4$  

Tags

CCSS.HSF.BF.B.5

Condense the expression as a single logarithm.

 $\ln4+\ln3x$  

•  $\ln7x$  

•  $\ln\left(3x\right)^4$  

•  $\ln12x$  

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Condense the expression as a single logarithm.

 $7\cdot\ln a-4\cdot\ln b$  

•  $\ln\ \frac{a^7}{b^4}$  

•  $\frac{7}{4}\ln\ \frac{a}{b}$  

•  $\ln\left(ab\right)^3$  

•  $\ln\left(ab\right)^{11}$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Expand the logarithmic expression.

 $\ln\left(2m^8\right)$  

•  $\ln2+\ln m^8$  

•  $\ln2-8\ln m$  

•  $\ln\ \frac{2}{m^8}$  

•  $\ln2+8\ln m$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Expand the logarithmic expression.


 $\ln\left(\frac{m^5}{n^2}\right)^3$  

•  $\ln\left(\frac{m^{15}}{n^6}\right)$  

•  $15\cdot\ln m-6\cdot\ln n$  

•  $15\cdot\ln m+6\cdot\ln n$  

•  $\ln m^{15}-\ln n^6$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

Expand ln xy²z³

• 6(lnx + lny - lnz)
• lnx + 2lny - 3lnz
• lnx + (1/2)lny + (1/3)lnz
• lnx + 2lny + 3lnz

Tags

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8

Solve the following equation for x.  Round your solution to two decimal places.
ln2x - ln41 = 2

• x = 0.36
• x = 151.48
• x = 41
• None of these are solutions

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4