Logarithmic Solutions

Algebra Level 2

If $\log_{2}{3}=a$ , then find the value of $\log_{0.2}{81}$ .

1

\dfrac {4a} {\log_{10}{2}}

\dfrac {4a-1} {\log_{2}{10}}

\dfrac {4a} {1-\log_{2}{10}}

1 solution

Hung Woei Neoh
May 12, 2016

$\log_2 3 = a$

$\log_{0.2} 81\\ =\dfrac{\log_2 81}{\log_2 0.2}\\ =\dfrac{\log_2 3^4}{\log_2 \frac{2}{10}}\\ =\dfrac{4 \log_2 3}{\log_2 2 - \log_2 10}\\ =\boxed{\dfrac{4a}{1-\log_2 10}}$

Logarithmic Solutions

1 solution

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