Exp and Log Functions

Rewrite as exponent.

 $\log_3\ 27\ =\ 3$  

•  $3^3\ =\ 27$  

•  $27^{3\ }=\ 3$  

•  $3^{27\ }=\ 3$  

•  $3^{3\ }=\ \frac{1}{27}$  

Tags

CCSS.HSF.BF.B.5

Rewrite as exponent.

 $\log_{\frac{1}{9}}81\ =\ -2$  

•  $-2^{\frac{1}{9\ }}\ =\ 81$  

•  $-2^{81}\ =\ \frac{1}{9}$  

•  $\left(\frac{1}{9}\right)^{-2}\ =\ 81$  

•  $81^{-2}\ =\ \frac{1}{9}$  

Tags

CCSS.HSF.BF.B.5

Rewrite as log.

 $12^2\ =\ 144$  

•  $\log_{144}\ 2\ =\ 12$  

•  $\log_{12}\ 144\ =\ 2$  

•  $\log_{12}\ 2\ =\ 144$  

•  $\log_2\ 12\ =\ 144$  

Tags

CCSS.HSF.BF.B.5

Rewrite as log.

 $7^{-2\ }\ =\ \frac{1}{49}$  

•  $\log_7\ \frac{1}{49}\ =\ -2$  

•  $\log_7\ -2\ =\ \frac{1}{49}$  

•  $\log_{\frac{1}{49}}7\ =\ -2$  

•  $\log_{-2}\ 7\ =\ \frac{1}{49}$  

Tags

CCSS.HSF.BF.B.5

Condense

 $\log_3\ 11\ +\ 6\log_3\ x$  

•  $\log_3\ 17x$  

•  $\log_3\ 66x$  

•  $\log_3\ x+11$  

•  $\log_3\ 11x^6$  

Condense

 $\ln8-3\ln x$  

•  $\ln\ \frac{x^3}{8}$  

•  $\ln\ \frac{8}{x^3}$  

• ln  $\ln\ \left(\frac{8}{x}\right)^3$  

•  $\ln\ \left(\frac{x}{8}\right)^3$  

Expand completely.

 $\log\ \frac{x}{2y}$  

•  $\log\ x-\log2y$  

•  $\log\ 2\ +\log y\ -\ \log\ x$  

•  $\log\ x\ -\ \log\ 2\ +\log\ y$  

•  $\log\ x\ -\ \log\ 2\ -\ \log\ y$  

Expand completely.

 $\ln\ 4x^2$  

•  $\ln\ 4+\ln x^2$  

•  $\ln\ 4\ +\ 2\ln x$  

•  $2\ln4+2\ln x$  

•  $\ln4\ -\ 2\ln x$  

Solve for x.

 $343^{\left(x+1\right)}=49^{\left(2x\right)}$ 

Solve for x.

 $\ln\left(11x-5\right)=\ln\left(x+15\right)$