CW: Rewriting & Evaluating Logs/Exponents

Logarithmic functions are the inverse of...

• Linear Functions
• Exponential Functions 
• Quadratic Functions 
• Polynomial Functions 

Tags

CCSS.HSF.BF.B.5

Write the logarithmic function in exponential form: $\log_{64}2=\frac{1}{6}$  

•  $64^2=\frac{1}{6}$  

•  $2^{\frac{1}{6}}=64$  

•  $64^{\frac{1}{6}}=2$  

•  $\frac{1}{6}^6=64$  

Tags

CCSS.HSF.BF.B.5

Rewrite in logarithmic form:

 $5^{-1}=\frac{1}{5}$  

•  $\log_5\left(\frac{1}{5}\right)=-1$  

•  $\log_{\frac{1}{5}}\left(-1\right)=5$  

•  $\log_5\left(-1\right)=\frac{1}{5}$  

•  $\log_{-1}\left(5\right)=\frac{1}{5}$  

Tags

CCSS.HSF.BF.B.5

Rewrite as a logarithm:

 $6^0=1$  

•  $\log_61=0$  

•  $\log_60=1$  

•  $\log_16=0$  

•  $\log_01=6$  

Tags

CCSS.HSF.BF.B.5

Rewrite as a logarithm:

 $32^{\frac{-1}{5}}=\frac{1}{2}$  

•  $\log_{\frac{1}{2}}32=\frac{-1}{5}$  

•  $\log_{32}\ \frac{1}{2}=\frac{-1}{5}$  

•  $\frac{1}{5}\log\ =\ 32^{\frac{1}{2}}$  

•  $\log_{-\frac{1}{5}}\ \frac{1}{2\ }=\ 32$  

Tags

CCSS.HSF.BF.B.5

Rewrite as a logarithm:

 $81^{\frac{3}{4}}=27$  

•  $\log_{81}27=\frac{3}{4}$  

•  $\log_{27}81=\frac{3}{4}$  

•  $\log_{\frac{3}{4}}27=81$  

•  $\log_{\frac{3}{4}}81=27$  

Tags

CCSS.HSF.BF.B.5

Solve: 9^8-x = 27^x-3

• x = 5
• x = -5
• x = 1/5
• x = -1/5

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Solve for x:
3^2x = 27^{x - 4}

• x = 12
• x = 4
• x = -4
• x = 1

Tags

CCSS.HSA.CED.A.1

CCSS.HSA.REI.A.1

CCSS.HSF.BF.B.5

CCSS.HSF.LE.A.4

Find the values of x when

 $49^{5x}=343^{\left(2x+1\right)}.$  

•  $x=-\frac{1}{2}$  

•  $x=\frac{1}{4}$  

•  $x=\frac{3}{4}$  

•  $x=\frac{5}{4}$  

Solve

 $27^x=81.$  

•  $x=\frac{4}{3}$  

•  $x=\frac{3}{4}$  

•  $x=-\frac{4}{3}$  

•  $x=-\frac{3}{4}$