Proving the laws of logarithm (SP4.10)

Given that  $\log_74=0.712$   and  $\log_7\ 5=0.827$  . Evaluate  $\log_7\ 1\frac{1}{4}$  .

(a)  

Given that  $\log_74=0.712$   and  $\log_7\ 5=0.827$  . Evaluate  $\log_7\ 28$  .

(a)  

Given that  $\log_74=0.712$   and  $\log_7\ 5=0.827$  . Evaluate  $\log_7\ 100$  .

(a)  

Given that  $\log_74=0.712$   and  $\log_7\ 5=0.827$  . Evaluate  $\log_7\ 0.25$  .

(a)  

Evaluate
  $\log_3\ 21\ +\ \log_3\ 18-\ \log_3\ 14$  
without using a calculator

(a)  

Evaluate
  $2\log_4\ 2\ -\frac{1}{2}\ \log_4\ 9+\ \log_4\ 12$  
without using a calculator

(a)  

Evaluate
  $\log_2\ 7\ +\ \log_2\ 12-\ \log_2\ 21$  
without using a calculator

(a)  

Evaluate
  $\log_5\ 6\ +\ \log_5\ \left(\frac{15}{2}\right)-\ 2\log_5\ 3$  
without using a calculator

(a)  

 All the following equivalent to 2 EXCEPT

•  $\log_5\left(\frac{75}{2}\right)+\log_5\ 2\ -\log_5\ 3$  

•  $\log_3\ 36+\log_3\ 5\ -\log_3\ 20$  

•  $\log_5\left(50\right)+\log_5\ 4\ -2\log_5\ 10$  

•  $\log_2\ 20\ -2\log_2\ 5+\log_2\ 5$  

Find the value of  $2\log_2\ 6\ +\log_{2\ }5\ -\log_2\ 45$  without using a calculator.

• 4

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• 5