Question

Find the value of log√3 (3√3) - log5 (0.04). ​

Answer 1

Answer:

The answer is 5

Step-by-step explanation:

   $\log_{\sqrt 3}(3\sqrt 3)-\log_5(0.04)$

 $=\log_{\sqrt 3}((\sqrt 3)^2\sqrt 3)-\log_5(\frac{4}{100})\\\\=\log_{\sqrt 3}(\sqrt 3)^ {2+1}-\log_5(\frac{1}{25})\\\\=\log_{\sqrt 3}(\sqrt 3)^ {3}-\log_5(\frac{1}{5^2})\\\\=\log_{\sqrt 3}(\sqrt 3)^ {3}-\log_5(5^{-2})\\\\=3\log_{\sqrt 3}(\sqrt 3)-(-2)\log_5(5)$

       $\boxed{\because \log_ab^n=n\log_ab }$

  $=3(1)+2(1)=5$

      $\boxed{\because \log_aa=1}$