Base e and Natural Logarithms

Write the equation in logarithmic form.
 $e^3=x$  

•  $\ln x=3$  

•  $\ln3=x$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Write the equation in logarithmic form.
 $e^x=36$  

•  $\ln36=x$  

•  $\ln x=36$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

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

CCSS.HSF.LE.A.4

 Write the equation in exponential form. 
 $\ln x=18$  

•  $x^{18}=e$  

•  $e^{18}=x$  

Tags

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

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

CCSS.HSF.LE.A.4

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.

 $\frac{1}{2}\cdot\ln256-3\cdot\ln2$  

•  $\ln128$  

•  $\ln8$  

•  $\ln32$  

•  $\ln2$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.BF.B.5

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.B.3

CCSS.HSF.BF.B.5

CCSS.HSF.IF.C.8